Name PID Section # (enrolled)

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1 STT 200 -Lecture 2 Instructor: Aylin ALIN 02/19/2014 Midterm # 1 A Name PID Section # (enrolled) * The exam is closed book and 80 minutes. * You may use a calculator and the formula sheet that you brought to the exam. * Table for the standard normal distribution is attached. * The exam has 40 multiple choice questions. Each question is 2.5 points. Total points possible for this exam is 100. * Answers recorded on the scatron and not on the test paper are the basis for scoring the exam. Use a pencil to mark your scatron. * Turn in your scatron when you exit the room. You may keep your exam paper and formula sheet. 1) The payroll amounts for all teams in an international hockey league are shown below using a graphical technique from chapter 2 of the text. How many of the hockey team payrolls exceeded $20 million (Note: Assume that no payroll was exactly $20 million)? 1) A) 10 teams B) 18 teams C)23 teams D) 8 teams 2) On a given day, the price of a gallon of milk had a mean price of $2.16 with a standard deviation of $0.07. A particular food store sold milk for $2.09/gallon. Interpret the z-score for this gas station. A) The milk price of this food store falls 7 standard deviations below the mean milk price of all food stores. B) The milk price of this food store falls 1 standard deviation below the milk gas price of all food stores. C)The milk price of this food store falls 1 standard deviation above the mean milk price of all food stores. D) The milk price of this food store falls 7 standard deviations above the mean milk price of all food stores. 2) 3) On a physical fitness test middle school boys are awarded one point for each push-up they can do, and a point for each sit-up. National results showed that boys average 18 pushups with a standard deviation of 4 push-ups, and 34 sit-ups with standard deviation 11. The mean of their combined (total) scores was therefore = 52 points. If for each boy push-ups and sit-ups are independent, what is the standard deviation of their combined scores? A) 15 B) 5.3 C)11.7 D) 137 3) 1

2 4) A researcher identified 100 men over forty who were not exercising and another 100 men over forty with similar medical histories who were exercising regularly. She followed all the men for several years to see if there was any difference between the two groups in the rate of heart attacks. This is a(n) A) prospective study. B) matched pairs experiment. C) survey. D) retrospective study. 4) 5) Which of the following statements is not true? A) Standardizing into z-scores do not change the shape of the distribution. B) Standard deviaiton is preffered over variance since it has the same unit with data. C) If 25% of your statistics class is sophomores, then in a pie chart representing classifications of the students in your statistics class the slice assigned to sophomores is 90 D) In skewed distributions, the mean is the best measure of the center of the distribution since it is least affected by extreme observations. 5) 6) A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next five free throw attempts? I. Let 0,1 represent making the first shot, 2, 3 represent making the second shot,, 8, 9 represent making the fifth shot. Generate five random numbers 0-9, ignoring repeats. II. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9. III. Let 0, 1, 2 represent missing a shot and 3, 4,, 9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats. A) II only B) III only C)I only D) I, II, and III 6) 7) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 85 jobs and a standard deviation of 5. Where do we expect approximately 95% of the distribution to fall? A) between 70 and 100 jobs per day B) between 75 and 95 jobs per day C)between 95 and 100 jobs per day D) between 80 and 90 jobs per day 8) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of ounces and a standard deviation of 0.20 ounce. Each can holds a maximum of ounces of soda. Every can that has more than ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process? A).3413 B).1587 C).6587 D) ) 8) 9) The five-number summary of credit hours for 24 students in a statistics class is: 9) Min Q1 Median Q3 Max Which statement is true? A) There are both low and high outliers in the data. B) There is at least one low outlier in the data. C)There are no outliers in the data. D) There is at least one high outlier in the data. 2

3 10) The January 2005 Gallup Youth Survey telephoned a random sample of 1,028 U.S. teens and asked these teens to name their favorite movie from Napoleon Dynamite had the highest percentage with 8% of teens ranking it as their favorite movie. Which is true? I. The population of interest is all U.S. teens. II. 8% is a statistic and not the actual percentage of all U.S. teens who would rank this movie as their favorite. III. This sampling design should provide a reasonably accurate estimate of the actual percentage of all U.S. teens who would rank this movie as their favorite. A) III only B) I only C)I and II D) I, II, and III 10) 11) A music store has 8 male and 12 female employees. Suppose one employee is selected at random and the employee's gender is observed. List the sample points for this experiment, and assign probabilities to the sample points. A) {8, 12}; P(8) =.5 and P(12) =.6 B) {male, female}; P(male) =.8 and P(female) =.12 C){male, female}; P(male) =.4 and P(female) =.6 D) {8, 12}; P(8) =.8 and P(12) =.12 11) 12) At a community college with 500 students, 120 students are age 30 or older. Find the probability that a randomly selected student is less than 30 years old. A).12 B).30 C).24 D).76 12) 13) The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $5 each, find the probability distribution for her daily profit. A) Profit P(profit) $300.5 $ $ C) Profit P(profit) $500.5 $ $ B) D) Profit P(profit) $100.5 $ $ Profit P(profit) $300.5 $ $ ) A(n) is the most basic outcome of an experiment. A) sample space B) experiment C) sample point D) event 13) 14) 15) A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in the state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: 15) A: {The home is constructed of brick} B: {The home is more than 30 years old} In terms of A and B, describe a home that is constructed of brick and is less than or equal to 30 years old. A) (A B)c B)A Bc C)A B D)A B 3

4 16) 16) For the distribution drawn here, identify the mean, median, and mode. A) A = mean, B = mode, C = median B) A = median, B = mode, C = mean C)A = mode, B = mean, C = median D) A = mode, B = median, C = mean 17) Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 250 students and carefully recorded their parking times. Identify the variable of interest to the university administration. A) the entire set of students that park at the university B) a single student that parks at the university C)the 250 students that data was collected from D) the parking time, defined to be the amount of time the student spent finding a parking spot 17) 18) A survey of some Stats students recorded gender and whether the student was left or right-handed. Results were summarized in a table like the one shown. If it turned out that handedness was independent of gender, how many of the Stats students were lefty girls? 18) A) 7 B) 9 C) cannot be determined D) 10 19) A study revealed that 45% of college freshmen are male and that 18% of male freshmen earned college credits while still in high school. Find the probability that a randomly chosen college freshman will be male and have earned college credits while still in high school. A) B) C) D) ) 20) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 3000 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty? A) 63,000 miles B) 65,250 miles C) 57,000 miles D) 54,750 miles 20) 4

5 21) A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows: 21) Number sold in a day Prob (Number sold) Find the number of cheesecakes that this local bakery expects to sell in a day. A) 10 B) 14.1 C) 20 D) ) A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 22) Find the upper quartile (Q3) of the data. A) 92 B) 81.5 C)73 D) ) Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The manager's educational background was also noted. The data appear below: 23) Educational Background Manager Rating H. S. Degree Some College College Degree Master's or Ph.D. Totals Good Fair Poor Totals What is the probability that a randomly chosen manager is either a good managers or has an advanced degree (Master's or PhD)? A) 147 B) 21 C) D) ) The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct? A) 50% of the students sampled had textbook costs that were less than $425 B) The most frequently occurring textbook cost in the sample was $425 C)The average of the textbook costs sampled was $425 D) 50% of the students sampled had textbook costs equal to $425 24) 25) A sample of 100 weights has Q1 = 150 lbs, Q2 = 165 lbs and Q3 = 190 lbs. The three largest weights in the sample are 230 lbs, 241 lbs and 275 lbs. The upper (right) whisker of the boxplot of the data extends to what value? 25) A) 250 B) 190 C)241 D) ) The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data. A) $250 B) $98.75 C) $99.37 D) $450 26) 5

6 27) A sociologist recently conducted a survey of senior citizens who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows: 27) Find the median of the observations. A) 77.5 B) 78 C)74 D) 77 28) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a company's success is customer service. A study was conducted to determine the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table: 28) Frequency of Use High Satisfaction level Medium Low TOTAL < 2 per month per month > 5 per month TOTAL A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that the customer expressed medium satisfaction with the company? A) B) C) 1 D) ) Which of the following summaries are changed by adding a constant to each data value? I. the mean II. the median III. the standard deviation A) I and III B) III only C)I and II D) I, II, and III 29) 30) Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment? 30) A)P(A) = 0, P(B) = 1 9, P(C) = 8 9 B)P(A) = - 1 4, P(B) = 1 2, P(C) = 3 4 C)P(A) = 1 5, P(B) = 1 9, P(C) = 1 6 D)P(A) = 1 10, P(B) = 1 10, P(C) = ) The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score? A) 78 B) 70.5 C) cannot be determined D) 99 31) 6

7 32) At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds? 32) Speeds: 72 mph, 108 mph, and 116 mph A) None of the three speeds is an outlier. B) 72 is the only outlier. C)72, 108, and 116 are all outliers. D) 72 and 108 are both outliers, but 116 is not. 33) A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the standard deviation of the distribution. 33) x p(x) A) 5.7 B) C) 6.41 D) ) A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is A) greater than 50%, since it appears that we are in a streak of heads. B) It cannot be determined. C)less than 50%, since '"tails" is due to come up. D) 50%. 34) 35) Suppose that for a certain experiment P(B) = 0.5 and P(A B) = 0.2. Find P(A B). A) 0.7 B) 0.1 C)0.3 D) ) 36) A survey was conducted to determine how people feel about the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. 36) Stem Leaf Calculate the value of the sample mean for the data given in the stem-and-leaf display? A) B) C) D) ) The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. Considering these two variables, number of courses would best be considered a variable and drive time would be considered a variable. A) discrete; discrete B) discrete; continuous C) continuous; continuous D) continuous; discrete 37) 7

8 38) Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is Given that the athlete has not taken this steroid, the probability of a negative test result is Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid? A) B) C) D) ) 39) The advantage of making a stem-and-leaf display instead of a dotplot is that a stem-and-leaf display A) satisfies the area principle. B) shows the shape of the distribution better than a dotplot. C) A stem-and-leaf display is for quantitative data, while a dotplot shows categorical data. D) preserves the individual data values. 39) 40) The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Suppose P(1) = P(2) = P(3) = P(4) = 1 16 and P(5) = P(6) = P(7) = P(8) = P(9) = P(10) = ) Find P(A) and P(B). A)P(A) =.0625; P(B) =.25 B)P(A) =.25; P(B) =.5 C)P(A) =.3125; P(B) =.5 D)P(A) =.3125; P(B) =.25 8

9 Answer Key Testname: MIDTERM-1-A 1) C 2) B 3) C 4) A 5) D 6) A 7) B 8) B 9) C 10) D 11) C 12) D 13) B 14) C 15) B 16) D 17) D 18) B 19) C 20) D 21) B 22) B 23) C 24) A 25) C 26) C 27) D 28) D 29) C 30) A 31) D 32) B 33) B 34) D 35) B 36) A 37) B 38) D 39) D 40) C 9