Name: Class: _ Date: _ AP Statistics - Random Variables (Multiple Choice) Identify the choice that best completes the statement or answers the question. 1. A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution: X 0 1 2 3 4 5 P(X) 0.24 0.37 0.20 0.11 0.05 0.03 What is the probability that a randomly chosen household has at least two personal computers? A. 0.19 B. 0.20 C. 0.29 D. 0.39 E. 0.61 2. A random variable X has a probability distribution as follows: X 0 1 2 3 P(X) 2k 3k 13k 2k Where k is a positive constant. The probability P(X < 2.0) is equal to A. 0.90. B. 0.25. C. 0.65. D. 0.15. E. 1.00. 1
Name: 4.X and Y are independent random variables, and a and b are constants. Which one of the following statements is true? A. B. C. D. E. 5. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is approximately normal with mean $360 and standard deviation $50. What is P(X > $400)? A. 0.2119 B. 0.2881 C. 0.5319 D. 0.7881 E. 0.8450 2
Name: 9. In the town of Tower Hill, the number of cell phones in a household is a random variable W with the following distribution: W 0 1 2 3 4 5 P(W) 0.1 0.1 0.25 0.3 0.2 0.05 The probability that a randomly-selected household has at least two cell phones is A. 0.20. B. 0.25. C. 0.55. D. 0.70. E. 0.80. 10. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to make a $20,000 profit. If it is cool that day, she expects to make a $5000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based upon historical records, the weather office has estimated the chances of a warm day to be 0.60; the chances of a cool day to be 0.25. What is the producer s expected profit? A. $5,000 B. $11,450 C. $13,000 D. $13,250 E. $15,050 4
Name: 13. A randomly chosen subject arrives for a study of exercise and fitness. Consider these statements. I. After 10 minutes on an exercise bicycle, you ask the subject to rate his or her effort on the Rate of Perceived Exertion (RPE) scale. RPE ranges in whole-number steps from 6 (no exertion at all) to 20 (maximum exertion). II. You measure VO2, the maximum volume of oxygen consumed per minute during exercise. VO2 is generally between 2.5 liters per minute and 6 liters per minute. III. You measure the maximum heart rate (beats per minute). The statement(s) that describe a discrete random variable are A. I. B. II. C. I, III. D. I, II, III. E. None of the statements describe a discrete random variable. 14. Let the random variable X represent the amount of money Dan makes doing lawn care in a randomly selected week in the summer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected week, Dan will make less than A. $144 B. $216 C. $255 D. $30 E. $360 15. A vending machine operator has determined that the number of candy bars sold per week by a certain machine is a random variable with mean 125 and standard deviation 7. His profit on each bar sold is $0.25, and it costs him $5.00 per week to maintain the machine and rent the space for it. What are the mean and standard deviation for Y = the profit he earns from this machine in a randomly-selected week? A. Mean = 31.25, Standard deviation $3.25 B. Mean = 31.25, Standard deviation $1.25 C. Mean = 31.25, Standard deviation $1.75 D. Mean = 26.25, Standard deviation $1.25 E. Mean = 26.25, Standard deviation $1.75 5
AP Statistics - Random Variables (Multiple Choice) Answer Section MULTIPLE CHOICE 1. ANS: D /D/Correct! 2. ANS: B /B/Correct! 3. ANS: B /B/Correct! Binomial probability formula: P(k successes in n trials when p = success in one trial) is. 4. ANS: B /B/Correct! When adding or subtracting random variables, variances add but standard deviations do not. 5. ANS: A /A/Correct! 6. ANS: C /C/Correct! The dealer must sample with replacement in order to meet the independence requirement for the binomial distribution. 7. ANS: E /E/Correct! ; 8. ANS: D /D/Correct! (d) is the essential difference between the binomial setting and the geometric setting. None of the other statements are true. 1
9. ANS: E /E/Correct! 10. ANS: B /B/Correct! 11. ANS: E /E/Correct! Since we are sampling without replacement, draws from the deck are not independent, violating one property of both binomial and geometric distributions. 12. ANS: A /A/Correct! Statements II and III are conditions for the geometric setting. (Statement II is only true for the binomial setting). 13. ANS: C /C/Correct! Variables in I and III take on discrete integer values, the variable in II is continuous (though actual values are limited by the measurement process, there are no explicit gaps between values). 14. ANS: C /C/Correct! z-value for 0.60 is 0.25. 15. ANS: E /E/Correct! 16. ANS: C /C/Correct! Fits all conditions for geometric setting. 2