12. Which is the most appropriate statistic to summary the association between the data for house value (unit: thousand dollars) and income (unit: thousand dollars)?
(A) Correlation
(B) Interquartile
(C) Mean
(D) Relative frequency
(E) Skewness

13. In a particular city, 20% of the residents commute to work by cars, 30% of the residents commute to work by public transportations, 10% the residents uses both. Determine the probability of a resident from this city commute to work either by cars or public transportations. (A) 0.1 (B) 0.2 (C) 0.3 (D) 0.4 (E) 0.7

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

15. A corporation produces electrical components utilizing three nonoverlapping work shifts. It is known that 50% of the components are produced during shift 1, 20% during shift 2, and 30% during shift 3. A further look at product quality reveals that 6% of the components produced during shift 1 are defective. The corresponding percentage for shift 2 is 8%. Shift 3, the late-night shift, produces a relatively large percentage, 15%, of defective components. Given that a defective component is found, what is the probability that it was produced during shift 3? (A) 0.150 (B) 0.176 (C) 0.290 (D) 0.330 (E) 0.495

16. An IRS auditor only has time to audit two of three tax returns. Suppose two of the tax returns show that the taxpayer owes the IRS. Assume that the IRS auditor is to randomly select two of the returns. Let R denote the event of refund and N denote the event of non-refund (owe). Define the random variable X to equal the number of tax returns among the two selected. What of the following statement is incorrect? (A) The outcome of this experiment is RR, NR, NN. (B) The possible outcome of \( X \) is 0, 1, 2. (C) \( \mathrm{P[RR] = 4 / 9} \) (D) \( \mathrm{P[NR] = 2 / 9} \) (E) \( \mathrm{P[NN] = 1 / 9} \)

17. 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. What of the following condition is not necessary for X to be a binomial random variable? (A) A passenger is considered as a trial. (B) Each trial has only two outcomes such as "show up" and "don't show up". (C) Each trial has the same probability of passenger not showing up. (D) Trials are uncorrelated. (E) Trials are independent.

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.

19. What of the following statement is incorrect for a normal random variable X? (A) The area under a normal curve needs to be less than 1. (B) The mean and median of X are equal. (C) The mean and mode of X are equal. (D) The normal curve is symmetry about mean. (E) The probability above the mean and below the mean has to be equal.

20. Assume the secondary fee (X) for a case for a real estate agency in a real estate agency follows a normal distribution with mean 66.2 thousand dollars and standard deviation 4.4 thousand dollars. Which of the following statement is incorrect? (A) The probability of this real estate agency will receive at least 70 thousand dollars equals 0.1949. (B) The probability of this real estate agency will receive exactly 74.82 thousand dollars equals 0.025. (C) The probability of this real estate agency will receive less than 62.4 thousand dollars equals 0.1949. (D) The probability of this real estate agency will receive less than 66.2 thousand dollars equals 0.5. (E) The probability of this real estate agency will receive more than 62.4 thousand dollars and less than 70 equals 0.6102.

21. What of the following condition is not necessary for the Central Limit Theorem? (A) Each observation has equal mean. (B) Each observation has equal variance. (C) Each observation has to have a normal distribution. (D) Observations are independent. (E) The sample size has to be large.

22. What of the following condition is not necessary for collecting the random samples? (A) Each observation has equal mean. (B) Each observation has equal variance. (C) Each observation has the same distribution. (D) Observations are independent. (E) The sample size has to be large

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