Chapter 4 and Chapter 5 Test Review Worksheet

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1 Name: Date: Hour: Chapter 4 and Chapter 5 Test Review Worksheet You must shade all provided graphs, you must round all z-scores to 2 places after the decimal, you must round all probabilities to at least 4 places after the decimal. 1. State whether the variable is discrete or continuous. x = The amount of money made by the school store this quarter. 2. State whether the variable is discrete or continuous. x = The number of people who attended the swim meet. 3. The table below shows the number of car accidents and their frequency among local high school students for one year. Accidents, x Number of Students, f a.) Construct a probability distribution for the table. Round each probability to 3 places after the decimal. Accidents, x Probability,P (x) b.) A student has one car accident in one year and claims that having 1 car accident is not unlikely. Determine if this student s claim is accurate. Use a number from the probability distribution you created in part a.) to support your answer. Explanation: 4. Determine the probability distribution s missing value. P(4) = x P(x) ? 1

2 5. Determine if the given distribution is a probability distribution. If not, identify ALL requirements not satisfied. You must use proper P(x) notation. x P(x) Explanation: 6. In a pizza takeout place, the following probabiilty distribution was obtained. The random variable x, represents the number of toppings for a large pizza. Find the mean and standard deviation. µ = Ê Ê ËÁ x P(x) ˆ = σ = Ê ËÁ x µ ˆ 2 ˆ P(x) ËÁ = x P(x) At a raffle, 1000 tickets are sold at $20 each for three prizes valued at $5,000, $1000, and $500. What is the expected value of one ticket? x P(x) E(x) = Ê ËÁ x P(x) ˆ = 2

3 8. Decide which probability distribution: binomial, geometric, or Poisson applies to the question. You do not need to find the probability. The average number of sales calls that are successful in a given day is 12. What is the probability that you will make exactly 10 successful sales calls tomorrow? 9. Decide which probability distribution: binomial, geometric, or Poisson applies to the question. You do not need to find the probability. The probability you make a successful sales call is 33%. If you make 100 sales calls in one day, what is the probability that exactly 50 of those calls will be successful? 10. Decide which probability distribution: binomial, geometric, or Poisson applies to the question. You do not need to find the probability. The probability that you make a successful sales call is 33%. What is the probability that you make your first sale on the 10th call? 11. Use either the binomial, geometric, or Poisson distribution to find the probability. Basketball player Chauncey Billups makes free throw shots 85% of the time. Find the probability that he misses his first 2 shots and makes his 3rd. DISTRIBUTION CHOICE: P( ) NOTATION: 12. Use either the binomial, geometric, or Poisson distribution to find the probability. The test consists of 8 multiple choice questions, each with 4 possible answers, one of which is correct. To pass the test a student must get 5 or more correct on the test. If the student randomly guesses, what is the probability that the student will pass the test. DISTRIBUTION CHOICE: P( ) NOTATION: 13. Use either the binomial, geometric, or Poisson distribution to find the probability. The mean number of business failures per hour in the U.S. was 5 last year. Assuming that the mean stays the same, what is the probability that more than 2 businesses will fail in the next hour? DISTRIBUTION CHOICE: P( ) NOTATION: 3

4 14. Using the normal probability table, find and shade the area under the standard normal curve to the right of z = Using the normal probability table, shade and find the sum of the areas under the standard normal curve to the left of z = -1 and to the right of z = Using the normal probability table, find and shade the area under the standard normal curve to determine the z-score that corresponds to a cumulative area of Using the normal probability table, find and shade the area under the standard normal curve to determine the z-scores for which 95% of the distribution s area lies between -z and z. 4

5 18. Using the normal probability table, find and shade the area under the standard normal curve to determine the z-score that represents the first quartile. 19. Using the normal probability table, find and shade the area under the standard normal curve to determine the z-score that represents the 40th percentile. 20. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individual s IQ score is found to be 150. Find the z-score corresponding to this value. 21. IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-value corresponding to a z-score of The distribution of cholesterol levels in teenage boys is approximately normal with a mean of 170 and a standard deviation of 30. Levels above 200 warrant attention. Find the probability that a teenage boy s cholesterol level is greater than

6 23. The distribution of cholesterol levels in teenage boys is approximately normal with a mean of 170 and a standard deviation of 30. Find the percentage of teenage boys cholesterol levels between 150 and An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean of 15.5 suitcases and a standard deviation of 3.6 suitcases. Find the probability that during a given week the airline will lose less than 10 suitcases. 25. Assume the salaries of elementary school teachers in the U.S. are normally distributed with a mean of $34,000 and a standard deviation of $2000. What is the cutoff salary, x, for teachers in the bottom 5% of salaries? 26. The per capita consumption of soft drinks by people in the U.S. in a recent year was normally distributed with a mean of 49.3 gallons, and a standard deviation of 17.1 gallons. Random samples of size 25 are drawn from this population and the mean of each sample is determined. Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. Include units. µ x = σ x = 27. The graph of the population distribution for snow fall (in feet) for a given county is below: Assume that a sample of size 100 is drawn from each population. With µ = 5.8 ft. σ = 2.3 ft. Find µ x = and σ x = and sketch the sampling distribution of sample means. µ x = σ x = 6

7 28. The distribution of room and board expenses per year a WMU is normally distributed with a mean of $5,850 and a standard deviation of $1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Use z-scores to determine which of the following mean expenses would be considered unusual, then circle it. A. $5,200 B. $6,175 C. $6,120 z = z = z = 29. Assume that the heights of men are normally distributed with a mean of 67.9 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean height greater than 68 inches. 30. Assume that the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches. If 64 men are randomly selected, find the probability that they have a mean heights between 68.5 and 69.5 inches. 7

8 ID: A Chapter 4 and Chapter 5 Test Review Worksheet Answer Section SHORT ANSWER 1. Continuous 2. Discrete 3. The student s claim is correct because there is about a 40% chance of that many accidents P(4) = Is NOT a probability distribution P(0) > 1 and P(2) < 0 and P(x) 1 6. µ = 1.44 σ = $ Poisson 9. binomial 10. geometric z = z = z = z = z = z = x = % $30, µ x = 49.3 σ x =

9 ID: A 27. µ x = 5.8ft ;σ x = 0.23ft 28. $5,200 is unusual

Exam II Math 1342 Capters 3-5 HCCS. Name

Exam II Math 1342 Capters 3-5 HCCS Name Date Provide an appropriate response. 1) A single six-sided die is rolled. Find the probability of rolling a number less than 3. A) 0.5 B) 0.1 C) 0.25 D 0.333 1)