Applied Mathematics 12 Extra Practice Exercises Chapter 3

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1 H E LP Applied Mathematics Extra Practice Exercises Chapter Tutorial., page 98. A bag contains 5 red balls, blue balls, and green balls. For each of the experiments described below, complete the given table to show the probability distribution. Classify each distribution as a uniform distribution, a binomial distribution, or neither. a ) A ball is randomly drawn from the bag and its colour is recorded. Colour Red Blue Green b) A ball is randomly drawn from the bag and its colour is recorded as either red or not red. Number of Red Balls c) A ball is randomly drawn from the bag and its colour is recorded as either green or not green. Number of Green Balls. Given the spinner below, construct a histogram to show the probability distribution for the outcome of one spin of the spinner. Is this a binomial distribution, a uniform distribution, or neither. Which of the following experiments may be classified as a binomial distribution Explain your answers. a ) Two coins are tossed times and the number of times that both of the coins land tails is recorded. b) A card is drawn from a well-shuffled standard deck of cards and the suit is recorded. This is repeated times and the cards are not replaced after each draw. c) A -sided die numbered from to and a regular 6-sided die are rolled together. This is repeated times and the number of times that a sum of 6 appears is recorded. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

2 Applied Mathematics Extra Practice Exercises Chapter d) A -question multiple-choice test has possible answers for each question. A student guesses the first 9 answers randomly but is certain of the answer to the tenth question. The number of correct answers is recorded. e) A curling team plays games in a tournament. The probability of the team winning the first game is 5%. If the team wins a game, their confidence increases and the probability of them winning their next game increases by %. The number of wins is recorded. f) In a light-bulb manufacturing plant, the probability of a bulb being defective is.%. A sample of bulbs is chosen at random and the number of defective bulbs recorded. g ) A basketball player makes 85% of her free throws. In a particular game she has free throws. The number of free throws that she makes is recorded.. Which of the following histograms show uniform distributions a) b) c) d) e) 5. Which of the following histograms show binomial distributions a) Theoretical probability b) of landing heads with the toss of coins Number of times a head appears of rain during the week of October 5th Rain No rain Rain or no rain Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 7

3 Applied Mathematics Extra Practice Exercises Chapter c) that a car d) salesperson sells a given number of cars in a week A charity is raffling off a new car and sells raffle tickets. Justin purchases 5 tickets. Complete the following table to show the probability distribution for Justin winning the car. Outcome Win Lose 7. The Twisters and the Gladiators play against each other in a rugby league. The Gladiators have won 8% of the games played to date. Use your calculator to construct a binomial distribution for the Gladiators winning the next 5 games, then complete this table. Number of Wins 5 8. According to weather statistics, the probability of rain in V ancouver on a day in the first week of March is 65%. Use your calculator to create a binomial distribution for the number of rainy days during this week and then complete the table below. Number of Rainy Days Number of cars sold that grade students in a class of are smokers Smokers Non-smokers Smokers or non-smokers Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 8

4 Applied Mathematics Extra Practice Exercises Chapter 9. A drug has a success rate of 7%. Six randomly selected patients who have used the drug are surveyed. Use your calculator to create a binomial distribution for the number of patients who may have been cured by the drug and then complete the table below. Number of Patients Cured 5 6. A basketball player makes 85% of her free throws. In a particular game she has 5 free throws. Use your calculator to create a binomial distribution for the number of free throws that she makes and then complete the table below. Number of Free Throws Made 5. The probability that a certain hitter in baseball will strike out is 5%. Use your calculator to create a binomial distribution for the number of times the hitter strikes out in a game in which he comes up to bat times. Complete the following table. Number of Strike-Outs. Use your calculator to construct a histogram for each of the following binomial experiments. In each case, n represents the number of trials and p represents the probability of success on a given trial. Indicate the probability of success on each bar of the histogram. a) n = and p =. b) n = 5 and p =.5 c) n = 6 and p =.5 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 9

5 Applied Mathematics Extra Practice Exercises Chapter. A weighted coin has a 6% probability of landing heads. Use your calculator to create a binomial distribution for the number of times the coin lands heads in 5 tosses. Represent your answer as a histogram.. A basketball player is successful on his free throws 7% of the time. In a particular game he has 8 free throws. a) Determine the probability that he makes all 8 free throws. b) Determine the probability that he makes at least of the 8 free throws. 5. The probability of an archer hitting a target is 85%. The archer takes shots at the target. a) Determine the probability that the archer hits the target on all shots. b) Determine the probability that the archer misses the target on all shots. 6. Calculate the probability of a family of 6 children having exactly boys. 7. Calculate the probability of having exactly days of rain in a week if the probability of rain on any one day is 75%. 8. A multiple-choice test has questions. There are choices for each question; only one is correct. Determine the probability of answering exactly questions correctly if each question is answered by random guessing. 9. A binomial experiment consists of 6 trials with a probability of success on each trial of.. a) Calculate the probability of obtaining exactly successes. b) Calculate the probability of obtaining at least successes. (Hint: add the probabilities for,, 5, and 6 successes.) c) Calculate the probability of obtaining less than successes. (Hint: add the probabilities for,, and successes.) Round your answers to decimal places.. The probability of a cow dying from a certain disease is 5%. A herd of cattle numbering cows contracts the disease. Determine the probability that at least half of the cows will die from this disease. Round your answer to decimal places. Tutorial., page 5. Calculate the mean and standard deviation for each of the following sets of data. a) 5, 85, 55, 9, 75,, 6, 5,, 8 b) 67, 78, 9, 8, 65, 88, 9, 8, 65, 77, 65, 95 c) 7.5, 6.8, 7., 6., 6., 6.8, 7., 7., 7., 6.6, 6.5, 7.8, 7., 6.8, 7. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 5

6 Applied Mathematics Extra Practice Exercises Chapter. Two archers shoot at their targets times, each from the same distance away. After shooting, the distance in centimetres from each arrow to the centre of the target is recorded. The results are as follows. Archer M:, 5,,, 5, 8, 5, 7, 5, Archer N: 5, 5, 65,, 8, 55,, 9, 5, 77 a) Calculate the mean and standard deviation for each set of data. b) Which archer will win if only the closest shots count towards their score c) Which archer is the most consistent shooter. The prices of cars available for sale at two different dealerships are listed below. Dealership A: $ 5, $, $, $ 55, $8 7, $ 5, $5 5, $, $, $ 5 Dealership B: $5 5, $, $ 5, $9 9, $8 9, $6 5, $55, $8 55, $5, $ 8 a) Calculate the mean and standard deviation for each set of data. b) Which dealership s prices have the greatest standard deviation. The heights, in metres, of 5 students were measured when they were in grade and again when they were in grade. The results are listed below. Grade :.,.,.,.5,.,.,.6,.,.,.,.,.,.,.,. Grade :.7,.6,.,.8,.6,.9,.8,.5,.,.7,.5,.7,.7,.5,.8 a) Calculate the mean and standard deviation for each set of data. b) Which of the two sets of data has the least standard deviation 5. Basil and Harry play a round of 8 holes of golf. Their scores for each hole are listed below. Basil:,, 5, 6,, 5,,, 6,,,,, 5, 5,,, Harry: 5,, 5,, 6,, 5,, 5,, 6, 5, 5,,,,, 5 a) Calculate the mean and standard deviation for each set of data. b) Which player won the round of golf c) Which player was the most consistent golfer 6. Calculate the mean and standard deviation for each of the following frequency tables. a) Value Frequency 8 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 5

7 Applied Mathematics Extra Practice Exercises Chapter b) c) d) Value Value Value Frequency 5 5 Frequency Frequency 5 5 e) Which of the frequency tables has the greatest standard deviation f) Which has the least standard deviation 7. A survey was conducted on a class of grade students on the number of hours of television viewed per weeknight. The results are shown in the table below. Construct a histogram for the data set and calculate the mean and standard deviation for the data. Hours 5 6 Frequency Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 5

8 Applied Mathematics Extra Practice Exercises Chapter 8. Two companies, A and B, manufacture ball bearings. A sample of ball bearings is taken from each company and the diameters measured accurately to the nearest.5 mm. The results are shown in the tables below. Company A Diameter (mm) Frequency 8 5 Company B Diameter (mm) Frequency 6 6 a) Calculate the mean and standard deviation for each set of data. b) Which company manufactures ball bearings with the most uniform size c) If the machines are to be set to produce ball bearings with a diameter of 6.5 mm, which company s machine would be the easiest to adjust Explain. 9. Three different groups of 5 mice were sent through a maze in an animal behaviour experiment. The time taken for each mouse to complete the maze was recorded. The results for each group of mice are given in the tables below. Group Time to Complete the Maze (min).5.5 Frequency 7 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 5

9 Applied Mathematics Extra Practice Exercises Chapter Group Time to Complete the Maze (min).5.5 Frequency 5 Group Time to Complete the Maze (min).5.5 Frequency 9 8 a) Determine the mean and standard deviation for each set of data. b) Which group of mice had the fastest mean time c) Which group of mice had the least consistent results. The masses of a sample of candy bars produced by machine A are measured and recorded. This process is repeated with a sample of candy bars produced by machine B. The mean masses for the candy bars produced by machines A and B are the same. The standard deviation for the candy bars produced by machine A is.5 g whereas the standard deviation for the candy bars produced by machine B is.5 g. Which machine do you think is in most need of repair Explain.. Ten professional golfers hit a golf ball and the length of each drive is recorded. This process is repeated with randomly selected golfers from a local golf course. Which group of golfers do you expect would have the greater standard deviation. Which of the following sets of data is likely to have the smallest standard deviation Use your calculator to check your prediction. Set A: 5, 5, 6, 6, 6, 6, 6, 7, 7, 8 Set B:, 5, 5, 8, 8,,,,,. Which of the following histograms is likely to have the greatest standard deviation and which is likely to have the least a) b) c) Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 5

10 Applied Mathematics Extra Practice Exercises Chapter. Which of the following frequency tables is likely to have the least standard deviation Use your calculator to check your prediction. Table Value 6 8 Frequency 5 5 Table Value 6 8 Frequency The values of n and p for different binomial distributions are given below. In each case, n represents the number of trials and p represents the probability of success on a given trial. Calculate the mean and standard deviation for each distribution. a) n =, p =.6 b) n =, p =.5 c) n =, p =.5 d) n = 5, p = A multiple-choice test has 5 questions. There are 5 choices for each question; only one is correct. Calculate the mean and standard deviation for this binomial distribution if each question is answered by random guessing. 7. A baseball player has a batting average of.55. This means that he has hit successfully 55% of the time. Calculate the mean and standard deviation for the number of times the ball is hit in times up to bat. 8. Calculate the mean and standard deviation for each of the following binomial experiments. a) A regular 6-sided die is rolled 5 times and the number of times a appears is recorded. b) A regular 6-sided die is rolled 5 times and the number of times an even number appears is recorded. c) A coin is tossed 5 times and the number of times the coin lands heads is recorded. d) A coin is tossed 5 times and the number of times the coin lands heads is recorded. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 55

11 Applied Mathematics Extra Practice Exercises Chapter 9. A manufacturer of computer chips has found that about.5% of the chips it produces are defective. a) Calculate the mean and standard deviation for the number of defective chips in a sample of. b) Calculate the mean and standard deviation for the number of chips that are not defective in a sample of.. a) The mean for a set of data in a binomial experiment with 5 trials is 5. What is the probability of success b) If the number of trials in the binomial experiment is increased to and the mean remains the same, calculate the probability of success.. A sample of bags of potato chips was found to have these masses, in grams. 8, 85, 88, 9, 76, 85, 9, 76, 78, 8, 8, 88, 75, 78, 77, 68, 7, 7, 8, 7 a) Calculate the mean and standard deviation of this data. b) What problems will be encountered if the standard deviation gets too high Explain. Tutorial., page. The following graph of a normal distribution has a mean of and a standard deviation of a) What percent of the data lies between 5 and 5 b) What percent of the data lies between and c) What percent of the data lies between and d) What percent of the data lies between and 5 e) What percent of the data is less than Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 56

12 Applied Mathematics Extra Practice Exercises Chapter. The following graph of a normal distribution has a mean of 8 and a standard deviation of a) What percent of the data lies between.5 and 8 b) What percent of the data lies between 9.5 and c) What percent of the data lies between 5 and 6.5 d) What percent of the data lies between and.5 e) What percent of the data lies between.5 and.5. The following graph of a normal distribution has a mean of and a standard deviation of a) What percent of the data lies between and b) What percent of the data lies between 8 and c) What percent of the data lies between and 8 d) What percent of the data is less than 6 e) What percent of the data is greater than. The following graph of a normal distribution has a mean of and a standard deviation of a) What percent of the data is greater than b) What percent of the data is greater than 6 c) What percent of the data is greater than 8 d) What percent of the data is less than 9 e) What percent of the data is less than 5 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 57

13 Applied Mathematics Extra Practice Exercises Chapter 5. The following graph of a normal distribution has a mean of 5. and a standard deviation of a) What percent of the data lies between 5.57 and 6.7 b) What percent of the data lies between.8 and 5.8 c) What percent of the data lies between.57 and 5.8 d) What percent of the data is greater than 5.57 e) What percent of the data is less than Determine the standard deviation for each of the following graphs of normal distributions. a) b) 68% 95% c) 9.85% Three sets of data are described. Match each data set with the graph most likely to represent its distribution. Use each graph only once. a) the heights of 5 women between the ages of 8 and b) the hair lengths of 5 people at a hockey game c) the body temperatures of 5 men in a theatre i) ii) iii) Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 58

14 Applied Mathematics Extra Practice Exercises Chapter 8. The mean and standard deviation of a set of heights are µ = 75 cm and σ = 5 cm. a) Sketch a normal curve to show the distribution of heights. Mark the points that are,, and standard deviations from the mean. b) Between which of these points does 68% of the data lie c) Between which of these points does 95% of the data lie d) Sixteen percent of the data lies to the right of which one of these points e ) Between which of these points does 99.7% of the data lie 9. The mean and standard deviation of a set of heights are µ = cm and σ = 5 cm. a) Sketch a normal curve to show the distribution of heights. Mark the points that are,, and standard deviations from the mean. b) Between which of these points does 95% of the data lie c) Between which of these points does 99.7% of the data lie d) Between which of these points, to the right of the mean, does.5% of the data lie e ) Between which of these points does 8.5% of the data lie There are possible answers.. The mean and standard deviation of a set of data are µ = and σ =. a) Sketch a normal curve to show the distribution of the data. Mark the points that are,, and standard deviations from the mean. b) Between which of these points does 95% of the data lie c) Between which of these points, to the right of the mean, does.5% of the data lie d) Between which of these points, to the right of the mean, does 5.85% of the data lie e ) Two and one-half percent of the data lies to the right of which one of these points. The mean and standard deviation of a set of data are µ = 8. and σ =.8. a) Sketch a normal curve to show the distribution of the data. Mark the points that are,, and standard deviations from the mean. b) Between which of these points does 95% of the data lie c) Between which of these points, to the left of the mean, does.5% of the data lie d) Between which of these points, to the right of the mean, does 5.85% of the data lie e ) Sixteen percent of the data lies to the left of which one of these points Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 59

15 Applied Mathematics Extra Practice Exercises Chapter. A group of golden retrievers, each years old, has a mean height of 8. cm and a standard deviation of.8 cm. a) What is the probability that a randomly selected dog will have a height between 77. cm and 85.8 cm b) What is the probability that a randomly selected dog will have a height greater than 8 cm c) What is the probability that a randomly selected dog will have a height less than 7.6 cm. A shipment of eggs has a normal distribution with a mean height of 5. cm and a standard deviation of. cm. a) Sketch a normal curve to show the distribution of heights. Mark points that are,, and standard deviations from the mean. b) What percent of the shipment has the heights indicated i) greater than 5. cm ii) less than.96 cm iii) between.96 cm and iv) between.8 cm and 5. cm 5. cm. Corn plants in a field have heights that are normally distributed with a mean height of 85. cm and a standard deviation of 5.5 cm. What percent of the plants have the following heights i) between 79.5 cm and ii) between 9.5 cm and 96 cm.5 cm iii) greater than 7 cm iv) less than.5 cm 5. A machine produces ball bearings with a mean diameter of.5 cm and a standard deviation of. cm. a) In a sample of ball bearings, how many are expected to have diameters between. cm and.5 cm b) In a sample of ball bearings, how many are expected to have diameters greater than.59 cm c) In a sample of ball bearings, how many are expected to have diameters less than.7 cm 6. The mean life expectancy of elephants in a certain protected wilderness area is estimated to be 66 years, with a standard deviation of.5 years. In a herd of 55 elephants in this area, how many are expected to live longer than 75 years 7. The masses of 8 female athletes were measured and found to be normally distributed. The mean mass of these athletes was 55 kg, with a standard deviation of 5 kg. a) How many of these athletes had masses between 5 kg and 65 kg b) How many of these athletes had masses greater than 65 kg c) How many of these athletes had masses less than kg Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

16 Applied Mathematics Extra Practice Exercises Chapter Tutorial., page 9. The graph below is the Standard Normal Distribution Curve. 99.7% within units of the mean 95% within units 68% within unit Determine the area under this curve for each of the following intervals. a) between z = and z = b) between z = and z = c) between z = and z = d) between z = and z = e) to the right of z = f) to the left of z = Standard deviation scale z. Calculate the z-score for each of the following. a) µ = 8, σ = 5, and x = b) µ = 5.5, σ =.5, and x = 5 c) µ = 6.5, σ =.8, and x = d) µ =.8, σ =.6, and x =. Calculate the area of the shaded region under each of the following standard normal distribution curves. a) b).5. c) d)..5 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

17 Applied Mathematics Extra Practice Exercises Chapter. Calculate the area of the shaded region under each of the following standard normal distribution curves. a) b).8.5 c) d) Calculate the area of the shaded region under each of the following standard normal distribution curves. a) b) c) d) A population is normally distributed with a mean of 5.8 and a standard deviation of.5. What is the probability that a randomly selected member of the population will have the following measures a) greater than 7 b) greater than 8 c) greater than 5 d) greater than 7. A population is normally distributed with a mean of 5 and a standard deviation of. What is the probability that a randomly selected member of the population will have the following measures a) less than b) less than c) less than d) less than 8 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

18 Applied Mathematics Extra Practice Exercises Chapter 8. A population is normally distributed with a mean of 6.8 and a standard deviation of.. What is the probability that a randomly selected member of the population will have the following measures a) between 7. and 8. b) between 6.5 and 6.7 c) between 6. and 7. d) between 7. and The mean monthly attendance at a sports arena is 85, with a standard deviation of 5. a) What is the probability that the monthly attendance will be less than 8 b) What is the probability that the monthly attendance will be more than 9. The mean height of a group of students is.7 m, with a standard deviation of. m. Assume the heights are normally distributed. a) What percent of the students have a height greater than.9 m b) What percent of the students have a height between.6 m and.8 m. The mean body temperature of a group of patients undergoing a medical study is 6.8 C, with a standard deviation of.8 C. a) What percent of the patients have a body temperature below 7. C b) What percent of the patients have a body temperature above 7. C c) If there are 5 patients in the study, how many are expected to have body temperatures less than 7. C. In a sample of Florida oranges, the mean mass is 985 g, with a standard deviation of 5 g. a) What percent of the oranges have a mass between 9 g and g b) How many are expected to have a mass between 9 g and g c) How many are expected to have a mass less than g. Statistics indicate that the mean time before the brakes of a certain automobile require servicing is 8 months, with a standard deviation of.5 months. a) What percent of these automobiles will need their brakes serviced in the first year b) In a sample of 5 automobiles, how many will need their brakes serviced in the first year. A company sells taco chips by the g bag. The mass of a bag of chips is normally distributed with a mean of 95 g and a standard deviation of 5 g. a) What percent of the bags have a mass greater than the label indicates Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

19 Applied Mathematics Extra Practice Exercises Chapter b) What percent of the bags have a mass less than the label indicates c) In a sample of bags, how many have a mass greater than g 5. The mean life of Brand X light bulbs is 85 h, with a standard deviation of h. A sample of light bulbs is taken. a) How many would you expect to fail in less than h b) How many would you expect to have a life between h and h 6. The mean pulse rate of humans at rest is approximately 7 beats per minute, with a standard deviation of beats per minute. a) An athlete at rest has a pulse rate of 6 beats per minute. What percent of humans at rest would have a pulse rate greater than that of this athlete b) In a sample of 5 million people at rest, how many would have a pulse rate less than beats per minute 7. The mean weight of infants at a certain age is.5 kg, with a standard deviation of. kg. a) In a sample of infants, how many would weigh between. kg and.6 kg b) In a sample of infants, how many would weigh less than kg c) In a sample of infants, how many would weigh more than kg 8. A manufacturer of ball bearings must reject those ball bearings that have a diameter less than.98 cm or greater than. cm. The diameters of the ball bearings are normally distributed with a mean diameter of. cm and a standard deviation of. cm. a) What percent of the ball bearings must be rejected b) In a sample of 5 ball bearings, how many are expected to be rejected 9. The mean score on Test A was 7% with a standard deviation of %. The mean score on Test B was 7% with a standard deviation of.5%. Annie achieves 8% on both of these tests. On which test did Annie perform better. The mean score on Test A was 65% with a standard deviation of 5%. The mean score on Test B was 6% with a standard deviation of 6%. Stefan achieved 7% on Test A and Renee achieved 68% on Test B. Which student gave the better performance Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 6

20 Applied Mathematics Extra Practice Exercises Chapter Tutorial.5, page 6. Which of the following binomial distributions can be approximated by a normal distribution In each case, n represents the number of trials and p represents the probability of success on a given trial. a) n = 5, p =.5 b) n =, p =.5 c) n =, p =.5 d) n =, p =.99 e) n =, p =.. The following data represent binomial distributions. In each case, n represents the number of trials, p represents the probability of success on a given trial, and x represents a given value. Calculate the z-scores for those that can be approximated by a normal distribution. a) n =, p =.5, x = 5 b) n = 5, p =.5, x = c) n =, p =., x = d) n =, p =.8, x = 9 e) n =, p =.8, x =. Use the results of exercise a, b, d, and e to estimate the probability that a random value lies within the given interval. a) n =, p =.5, x > 5 b) n = 5, p =.5, x < c) n =, p =.8, 9 < x <. A multiple-choice test has questions. There are choices for each question; only one is correct. Leigh-Ann answers each question by random guessing. Estimate the following probabilities. a) Leigh-Ann answers less than 5 questions correctly. b) Leigh-Ann answers less than questions correctly. 5. A multiple-choice test has 65 questions. There are 5 choices for each question; only one is correct. Mike answers each question by random guessing. Estimate the following probabilities. a) Mike answers less than questions correctly. b) Mike answers less than questions correctly. c) Mike answers between 5 and questions correctly. 6. A fair coin is tossed 5 times and the number of times the coin lands tails is recorded. Estimate the following probabilities. a) The coin lands tails less than times. b) The coin lands tails more than times. c) The coin lands tails between and times. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 65

21 Applied Mathematics Extra Practice Exercises Chapter 7. In a baseball hitting challenge, the probability that Max will get a hit is 78%. If Max is thrown fair pitches, estimate the following probabilities. a) Max hits at least pitches. b) Max hits at most 5 pitches. c) Max hits between and 5 pitches, inclusive. 8. A study of a new drug is conducted on a group of patients. It was concluded that the probability of a certain patient recovering is 65%. Estimate the following probabilities. a) At least 5 patients will recover. b) At least patients will recover. c) Less than 5 patients will recover. d) Between and 5 patients will recover. 9. Use the normal approximation to a binomial distribution to estimate the following probabilities. a) A 6 is obtained between and times when a regular 6-sided die is rolled 5 times. b) A double 6 is obtained less than 5 times when two regular 6-sided dice are rolled times.. The probability of a certain computer chip being defective is.5%. A sample of computer chips is taken. Estimate the following probabilities. a) There will be less than 5 defective chips. b) There will be more than defective chips. c) There will be between and 6 defective chips, inclusive.. A manufacturer of bread machines estimates that one in a hundred machines will be defective. In a production run of machines, estimate the probability that no more than 5 will be defective.. Given that there is a 5% probability of a person being left-handed, estimate the following probabilities. a) More than people are left-handed in a group of. b) Between 5 and people are left-handed in a group of.. A survey indicates that 55% of people prefer low-fat milk to full-fat milk. Estimate the probability that in a sample of 6 people, between and people, inclusive, will prefer low-fat milk.. Customs officers at a certain international border crossing estimate that % of people are smuggling undeclared items. If people are searched at random, estimate the following probabilities. a) At least 5 people are smuggling. b) Between and people are smuggling. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 66

22 Applied Mathematics Extra Practice Exercises Chapter 5. Seventy-eight percent of families in a certain Canadian city own at least one car. Estimate the probability that in a random sample of families in the city, fewer than do not own at least one car. Tutorial.6, page. Construct a 95% confidence interval for each set of information given below. a) µ = 5, σ = b) µ = 8, σ = 5 c) µ = 5.8, σ =. d) µ =, σ = 5. Calculate the margin of error and the percent margin of error for each set of information given below. a) n =, σ = 5 b) n = 5, σ =.5 c) n =, σ = d) n = 5, σ =.5. Construct a 95% confidence interval for each set of information given below. a) n =, p =.8 b) n =, p =.5 c) n = 8, p =. d) n =, p =.5. Calculate the margin of error and the percent margin of error for each set of information given below. a) n = 5, p = 9% b) n = 5, p = 78% c) n =, p = 5% d) n =, p = % 5. Construct a 95% confidence interval for each set of information given below. In each case, n represents the total number of people polled in a survey and r represents the number of people who replied yes to the question. a) n =, r = 5 b) n = 5, r = 5 c) n =, r = A sample of 5 trees in a logging area has a mean diameter of 5 cm, with a standard deviation of 8.5 cm. a) Construct a 95% confidence interval for this data. b) Calculate the percent margin of error for this data. 7. A survey indicates that the mean purchase price for a house in an area south of Edmonton is $95, with a standard deviation of $5. a) Construct a 95% confidence interval for this data. b) Calculate the margin of error for this data. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 67

23 Applied Mathematics Extra Practice Exercises Chapter 8. The mean waiting time in July for a vehicle to cross the Canadian American border between the hours of 6: p.m. and 9: p.m. is 5 min, with a standard deviation of min. Construct a 95% confidence interval for a random sample of 5 vehicles and calculate the percent margin of error. 9. In a survey of 5 students at Carson High School, it was found that 5% of these students smoked cigarettes. Construct a 95% confidence interval for this data and calculate the percent margin of error.. A stereo salesperson estimates that he can make a sale to 5% of his interested customers. The salesperson deals with customers a day. a) How many sales can the salesperson expect in the average day b) Construct a 95% confidence interval for his daily sales.. A survey of 5 grade high school students in Calgary showed that of these students had already obtained their driver s licence. Construct a 95% confidence interval for this data.. In a survey of a random sample of teenagers in Nanaimo, B.C., it was found that 5 of these teenagers had never travelled outside of their own province. Construct a 95% confidence interval for this data.. Two surveys were taken in which the participants were asked, Have you ever had a speeding ticket. The results of Survey A showed that 5 out of people had received a speeding ticket. The results of Survey B showed that 8 out of 5 people had received a speeding ticket. Calculate the percent margin of error for each survey and state which survey was the most reliable.. A survey of 6 randomly selected British Columbians shows that 65% of people in B.C. use the internet. A survey of 8 randomly selected Canadians shows that 5% of Canadians use the internet. Calculate the percent margin of error for each survey and state which survey is the most reliable. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE EXERCISES 68

24 Applied Mathematics Extra Practice Answers Chapter Tutorial.. a) b) c) Neither Colour Red Blue Green Number of Red Balls Binomial and uniform Binomial Number of Green Balls 5 7. that a spinner lands on a certain number with one spin Neither. a, c, f, g. b, c 5. a, d Number that spinner lands on 6. Outcome Win Lose 5 95 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 69

25 Applied Mathematics Extra Practice Answers Chapter Number of Wins 5 Number of Rainy Days Number of Patients Cured 5 6 Number of Free Throws Made Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 7

26 Applied Mathematics Extra Practice Answers Chapter. Number of Strike-Outs a ) of success Number of trials b) c) of success of success Number of trials Number of trials Number of times coin lands heads. a ).58 b) a ).97 b) Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 7

27 Applied Mathematics Extra Practice Answers Chapter 9. a).8 b) =.99 c) = =.9 Tutorial.. a) 7.8,.6 b) 8,. c) 6.96,.5. a) M:.,.7 N: 9.8, 9.9 b) Archer N c) Archer M. a) Lot A: $5., $977.6 Lot B: $7 65., $ b) Lot A. a) Grade :.9,. Grade :.6,.6 b) Grade 5. a) Basil:.9,.8 Harry:.,.96 b) Basil c) Harry 6. a) 6.56,.5 b) 7.7,. c) 7.5,.75 d) 7.5,.5 e ) d f) b 7..66,.6 8 Frequency Hours watched 6 Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 7

28 Applied Mathematics Extra Practice Answers Chapter a) Company A: 5.95,.7 Company B: 5.78,.76 b) Company B c) Company B. This machine has the smallest standard deviation and is therefore the most consistent. 9. a) Group :.8,.56 Group :.5,.5 Group :.,.7 b) Group c) Group. Machine B because it produces the candy bars with the least consistent masses or highest standard deviation.. The ten golfers chosen at random from a local golf course would have the greater standard deviation.. Set A. Histogram a; Histogram b. Table 5. a) 6,.59 b) 5,.96 c),.8 d) 7.5,.5 6.,.88 7.,.5 8. a) 8.,.65 b) 5,.56 c) 5,.56 d) 5,.8 9. a) 5,. b) 995,.. a) p =.5 b) p =.5. a) 8 g, g b) Answers may vary. Tutorial.. a) 68% b) 95% c) 7.5% d) 9.85% e) 5%. a) 9.85% b).5% c).5% d).5% e) 99.7%. a) % b) 8.5% c) 5.85% d).5% e) 6%. a) 5% b) 97.5% c).5% d) 6% e) 8% Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 7

29 Applied Mathematics Extra Practice Answers Chapter 5. a) 5.85% b) 95% c) 97.5% d) 6% e) 97.5% 6. a).5 b).5 c). 7. a) (ii) b) (iii) c) (i) 8. a) Height (cm) 9. a) b) 7 and 8 c) 65 and 85 d) 8 e) 6 and Height (cm). a) b) 5 and 5 c) 5 and 75 d) 5 and 5 e) 75 and 5 or 5 and b) 8 and c) and d) and e). a) b) 7.6 and 85.8 c) 7.8 and 7.6 d) 8 and 88.6 e) 77. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 7

30 Applied Mathematics Extra Practice Answers Chapter. a).85 b).6 c).5. a) b) (i) 6% (ii).5% (iii)8.5% (iv) 8.85%. (i) 8.5% (ii) 5.85% (iii)97.5% (iv) 99.85% 5. a) 75 b).5 c) Height (cm) 7. a) 76 b) c) Tutorial.. a).68 b).985 c).975 d).585 e).9985 f).6. a) b).8 c).9 d).. a) b).8 97 c) d) a) b).6 9 c) d) a).56 8 b) c). 7 d) a).9 b).7 c).7 d) a).665 b).89 c).85 d) a).668 b).7 c).9876 d) a).9 b).95. a) 5.87% b) 8.9% Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 75

31 Applied Mathematics Extra Practice Answers Chapter. a) 99.8% b).6% c) 97. a) 56.% b) 56 c) 65. a).8% b). a) 5.87% b) 8.% c) a) 98 b) a) 99.5% b) 6 7. a) 6 b) 5 c) 5 8. a).55% b) 7 9. Test A. Stefan Tutorial.5. b, c. a). b).58 c) Cannot be approximated by a normal distribution d).69 e).99. a).6 b). 9 c) a) Extremely close to % b). 5. a).76 b).985 c) a). 5 b).786 c) a).9987 b) 5. 9 c) a).5 b).9999 c) V ery close to d) a).65 b).99. a).5 b).9999 c) a).99 b) a).98 b) Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 76

32 Applied Mathematics Extra Practice Answers Chapter Tutorial.6. a) 6.8 to 5.9 b) 7. to 89.8 c) to 5.89 d) 9.6 to 9.. a) ±9.8, ±.9% b) ±.9, ±.98% c) ±78., ±7.8% d) ±.98, ±.96%. a) 7.6 to 87.8 b) 6. to 89.7 c) to.5 d) 6.9 to a) ±.58, ±8.6% b) ±8.55, ±.6% c) ±.5, ±.5% d) ±7.5, ±.87% 5. a) 5.8 to.67 b) 9.96 to 7.8 c) to a) 5. cm to cm b) ±6.66% 7. a) $9 to $99 9 b) ±$ min to 8.9 min, ±.78% 9..5 to 6.95, 7.6%. a) 5 b).88 to to to 5.5. A: ±.58% B: ±5.% A is the better survey.. BC: ±.8% Canada: ±.6% The Canadian survey is the most reliable. Copyright Pearson Education Canada Inc., Toronto, Ontario EXTRA PRACTICE ANSWERS 77