14. Many organizations require their employees to be screened for drugs. Some employees are concerned that a “false positive” may be recorded from the screening; that is, employees who are not drug abusers may incorrectly test positive. Assume that 10% of a certain population are drug abusers. Suppose that the probability of a “false positive” is .5% and that the probability of a correct positive on someone who is under the influence of certain drugs is 99.9%. What is the probability that a person who tests positive is really a drug user? (A) 0.0045 (B) 0.0999 (C) 0.1000 (D) 0.9569 (E) 0.9990

18. Airline overbooking is a common practice. Many people make reservations on several flights due to uncertain plans and then cancel at the last minute or simply fail to show up. Eagle Air is a small commuter airline. Its planes hold only 15 people. Past records indicate that 20% of the people making a reservation do not show up for the flight. Let X denote the number of people making a reservation but do not show up for the flight out of 15 passengers. Assume X is a binomial random variable. What of the following statement is incorrect? (A) On a given flight, the probability that all passengers have seats is $0.2^{15}$. (B) The mean number of people making a reservation but do not show up for the flight equals 3. (C) The mean number of people making a reservation and show up for the flight equals 12. (D) The standard deviation of X equals 1.549. (E) The variance of X equals 2.4.

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