AP STATISTICS TEST (Chaps 1-7)

1. The National Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 and the standard deviation is 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure for these executives is 126.07. Which of the following is true? A. 128, 15, and 126.07 are statistics. B. 128 is a statistic; 15 and 126.07 are parameters. C. 128 and 15 are statistics; 126.07 is a parameter. D. 128 is a parameter; 15 and 126.07 are statistics. E. 128 and 15 are parameters; 126.07 is a statistic.

2. A student investigating study habits asks a simple random sample of 36 students at her school how many minutes they spent on their English homework the previous night. Suppose the actual parameter values for this variable are µ = 45 minutes and σ = 15 minutes. Which of the following best describes what we know about the sampling distribution of means for the student’s sample? A. = 45; unknown; shape of distribution unknown B. = 45; = 15; distribution approximately Normal C. = 45; = 15; shape of distribution unknown D. = 45; = 2.5; distribution approximately Normal E. = 45; = 2.5; shape of distribution unknown

3. The number of calories in a one-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12. For breakfast, you eat one ounce of the cereal with a cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast. The standard deviation of T is A. 22 B. 15.6 C. 11 D. 10.4 E. 12.1

4. The total sales on a randomly-selected day at Joy’s Toy Shop can be represented by the continuous random variable S, which has a Normal distribution with a mean of $3600 and a standard deviation of $500. Find P(S > $4000) A. 0.0668 B. 0.2514 C. 0.7486 D. 0.2119 E. 0.7881

5. A standard deck has 52 cards (26 red and 26 black). Draw a card from a standard deck, observe the card, return the card to the deck, and shuffle. Count the number of times you draw a card in this manner until you observe a red. Which of the following best describes this setting? A. Y has a binomial distribution with n = 52 observations and probability of success p = 0.5. B. Y has a binomial distribution with n = 26 observations and probability of success p = 0.5. C. Y has a normal distribution with n = 52 observations and probability of success p = 0.5. D. Y has a geometric distribution with probability of success p = 0.5. E. none of the above

6. Select a random integer from –100 to 100. Which of the following pairs of events are mutually exclusive (disjoint)? A. A: the number is odd; B: the number is 5 B. A: the number is even; B: the number is greater than 10 C. A: the number is less than 5; B: the number is negative. D. A: the number is above 50; B: the number is less than 20. E. A: the number is positive; B: the number is odd.

7. You work for an advertising agency that is preparing a new television commercial to appeal to women. You have been asked to design an experiment to compare the effectiveness of three versions of the commercial. Each subject will be shown one of the three versions and then asked her attitude toward the product. You think there may be large differences between women who are employed outside the home and those who are not. Because of these differences, you should use A. a completely randomized design. B. a categorical variable. C. a block design. D. a stratified design. E. a multistage sample. AP STATISTICS TEST (Chaps 1-7)

8. For children between the ages of 18 months and 29 months, there is an approximately linear relationship between height and age. The relationship can be represented by = 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Loretta is 20 months old and is 80 centimeters tall. What is her residual? A. 2.47 B. 2.47 C. –12.60 D. 12.60 E. 77.53

9. The mean height of players in the National Basketball Association is about 79 inches and the standard deviation is 3.5 inches. Assume the distribution of heights is approximately Normal. Let H = the height of a randomly-selected NBA player. Find P(H > 74). A. 0.9236 B. 0.0764 C. 0.1015 D. 0.8554 E. None of these

10. A small company that prints custom t-shirts has 6 employees, one of whom is the owner and manager. Suppose the owner makes $120,000 per year and the other employees make between $40,000 and $50,000 per year. One day, the owner decides to give himself a $30,000 raise. Which of the following about salaries is true? A. The mean and median would change, but the standard deviation and inter-quartile range would not. B. The mean and the standard deviation would change, but the median and inter-quartile range would not. C. The mean and the inter-quartile range would change, but the median and standard deviation would not. D. The median and inter-quartile range would change, but the mean and standard deviation would not E. The mean, median, standard deviation, and inter-quartile range all change.

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1. In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below.

C $0 $500 $1000 $2000 P(C) 0.60 0.05 0.13 0.22 a. P(C > $500) b. Find the expected value of C. c. Find the standard deviation of C.

2. The Census Bureau reports that 27% of California residents were born outside the United States. Suppose that you choose four Californians independent of each other and at random. Let F = the number of foreign-born people in a randomly-selected group of four. (a) Find the probability that exactly one is foreign. (b) Find the probability that more than one is foreign. (c) Find the expected value of F. (d) Find the standard deviation of F.

3. The Internal Revenue Service estimates that 8% of all taxpayers filling out long forms make mistakes. An IRS employee starts to randomly select forms—one at a time—to check for mistakes. (a) What is the probability that the first form with mistakes is the 7th one she checks? (b) What is the probability that it takes more than 4 forms to find one with mistakes? (c) Suppose she grabs a stack of 20 forms. What is the probability that no more than 5 have mistakes?

4. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65 grams (g) and standard deviation 5 g. (a) Calculate the probability that a randomly selected egg weighs between 62.5 g and 68.75 g. (b) Think of cartons of such eggs as SRSs of size 12 from the population of all eggs. Calculate the probability that the mean weight of the eggs in a carton falls between 62.5 g and 68.75 g.