Test 6D (cumulative) AP Statistics Name:

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1 Test 6D (cumulative) AP Statistics Name: Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A hat holds a large number of slips of paper, each with a single digit from 1 to 4 on it. Which one of the following is a possible probability distribution for the number on a single randomly-selected slip of paper? (a) P() (b) P() (c) P() (d) P() (e) P() Jocelyn runs a small mail-order bumper-sticker business. Based on daily sales figures for the past two years, she has developed the following probability distribution for = daily profit (in dollars) P() Which of the following is the expected value of. (a) $3.25 (b) $10 (c) $13 (d) $15 (e) $18 3. John maintains two separate lines of lobster traps in Penobscot Bay. The East Bay traps produce a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds. The West Bay traps produce a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds. Which of the following are the mean and approximate standard deviation of the total weight of lobsters John traps in a day? (a) Mean = 11; Standard deviation = (b) Mean = 11; Standard deviation = 8.32 (c) Mean = 22; Standard deviation = 5.75 (d) Mean = 22; Standard deviation = 8.32 (e) Mean = 22; Standard deviation = Capital Car Wash sells a membership card for $25 per year that entitles the buyer to a $2 discount on each car wash purchased during the year. The number of times Danica washes her car has a mean of 15 with standard deviation of 4. What are the mean and standard deviation of the net gain Danica receives if she buys a membership card? (a) Mean = 5; Standard deviation = 4 (b) Mean = 5; Standard deviation = 8 (c) Mean = 30; Standard deviation = 4 (d) Mean = 30; Standard deviation = 8 (e) There is not enough information to determine both values.

2 5. A voting rights group randomly selects one individual voter from each of 20 different voting districts in a small city and asks him or her if they voted in the last national election. Let = the number of people in the sample of 20 who voted. Which, if any, of the following requirements for to be a binomial random variable is violated in this setting? (a) Two possible outcomes for each trial. (b) Each trial is independent of other trials. (c) The probability of success is the same for each trial. (d) The number of trials is fixed. (e) All requirement are met in this setting. 6. An inspector examines a large shipment (several thousand) of laser pointers by randomly selecting a pointer, one at a time, until he finds one that is defective. Suppose that 1% of the laser points are defective. Which one of the following expressions describes the probability that the first defective pointer he finds is the sixth one that he selects? 5 (a) ( 0.01) ( 0.99 ) 6 (b) ( 0.01) ( 0.99 ) (c) ( ) (d) ( 0.99) ( 0.01 ) 5 (e) ( 0.99) ( 0.01 ) 7. The mean weight of pomegranates grown in a certain orchard is 16.5 ounces, with a standard deviation of 3.2 ounces. Which of the following best describes the mean and standard deviation of the standard scores of these pomegranates? (a) µ = 16.5; σ = 3.2 (b) µ = 1; σ = 1 (c) µ = 1; σ = 0 (d) µ = 0; σ = 3.2 (e) µ = 0; σ = 1 8. Which of the following is the most important reason for randomly assigning subjects to treatment groups in an experiment? (a) To create groups that are as similar as possible. (b) To eliminate bias. (c) To create a double-blind design. (d) To reduce random variation. (e) To counteract the placebo effect.

3 9. If P( A) = 0.6; P( B) = 0.2, and P( A B) = 0.10, which of the following must be true? (a) A and B are independent and mutually exclusive. (b) A and B are not independent, but they are mutually exclusive. (c) A and B are independent, but they are not mutually exclusive. (d) A and B are neither independent nor mutually exclusive. (e) A and B are mutually exclusive, but there is not enough information to determine if they are independent. 10. Mr. Lee has just collected his last batch of 24 English essays, all of them as computer files. He s curious about how long the papers are, but he doesn t want to be fooled by large font sizes, so he uses the word processing software s word count feature. Below is a histogram of the word counts for the 24 essays. Which of the following best describes the distribution the variable Number of Words in these essays? (a) Skewed right, centered at about 750, with one high outlier. (b) Skewed left, centered at about 750, with one high outlier. (c) Skewed right, centered at about 850, with one high outlier. (d) Skewed left, centered at about 850, with one high outlier. (e) Skewed left, centered at about 850, with no outliers.

4 Part 2: Free Response Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 11. Six percent of the computer chips produced by Cheapo Chips are defective. Each month a random sample of 200 chips manufactured in that month is taken. Let = the number of defective chips in the sample. (a) What are the mean and standard deviation of? (b) Find the probability that 8 or fewer chips in a sample of 200 are defective. (c) In an effort to reduce the percentage of defective chips, the company contracts with a new supplier for some important components. In the next month, the sample of 200 chips has only 8 defective ones. Can the company conclude that the new components have reduced the rate of defective chips produced? Explain.

5 12. Andrea and Ashley are middle-distance runners for their school s track team. Andrea s times in the 400-meter race are approximately Normally distributed with a mean of 62 seconds and a standard deviation of 0.8 seconds. Ashley s times are approximately Normally distributed with a mean of 62.8 seconds and a standard deviation of 1 second. (a) The school record for the 400-meter is 60.0 seconds. What is the probability that Andrea breaks the record in her next race? (b) Assuming that Andrea and Ashley s times in any race are independent, what is the probability that Ashley beats Andrea in their next race?

6 13. How important is it to change your oil? A car dealer takes a random sample of people who bought cars from the dealership five years ago and asks them: 1) how many times they changed their oil in the first three years they owned the car, and 2) how many times they brought their cars to a repair shop for anything other than routine maintenance in the first five years. The results are provided in the scatterplot and computer output for regression below. Predictor Coef SE Coef T P Constant Oil Changes S = R-Sq = 29.6% R-Sq(adj) = 25.7% (a) Describe what the scatterplot reveals about the relationship between the frequency of oil changes and the frequency of service appointments. (b) Find the equation of the least-squares regression line, and interpret the slope of the line. (c) The car dealer prints a poster of this scatterplot and displays in their service department with the legend, You can pay us a little now, or you can pay us more later! Changing your oil more often will reduce the number of service appointments for your car! Comment on whether they have evidence to support this claim.

Statistics Summary Exercises

Statistics Summary Exercises 1. A marketing firm wants to determine the typical amount spent during a visit to the grocery store. Each day for one week, they record the amount spent by the first 25 shoppers at a major grocery store.