Name:_________________________________1(point) True/False: (Each question is worth 2 points) Indicate whether the statement is true or false. ____ 1. The length of time for which an apartment in a large complex remains vacant is a discrete random variable. ____ 2. We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable. ____ 3. Two events A and B are said to be independent if P(A|B) = P(B). ____ 4. If the random variable X is exponentially distributed with parameter = 2, then the probability that X is between 1 and 2 equals the probability that X is between 2 and 3. ____ 5. The sample size needed to estimate the population mean was found to be 865. If the value of the population standard deviation was 75, and the maximum allowable error was 5, then the confidence level used was 95%. ____ 6. If X and Y are two variables with correlation = 0.78. ____ 7. The standard error of the sampling distribution of the sample proportion , when the sample size n = 100 and the population proportion p = 0.30, is 0.0021. ____ 8. If you add two single probability distributions together you get a bivariate distribution. ____ 9. The sample proportion variance of , , and COV(X, Y) = 14.703, then the coefficient of is a consistent estimator of the population proportion p because it is unbiased and the is p(1 p) / n, which grows smaller as n grows larger. ____ 10. Suppose we have two events A and B. We can apply the addition rule to compute the probability that at least one of these events occurs. Multiple Choice: (Each question is worth 5 points) Identify the choice that best completes the statement or answers the question. ____ 11. If A and B are mutually exclusive events with P(A) = 0.75, then P(B): a. can be any value between 0 and 1. b. can be any value between 0 and 0.75. c. cannot be larger than 0.25. d. equals 0.25. ____ 12. A sample of size 200 is taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion is between 0.58 and 0.62 is: a. b. c. d. .02000 0.0320 .4314 None of these choices. ____ 13. If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is: a. 0.56 b. 0..70 c. 0.79 d. 0.93 ____ 14. If two random samples of sizes n1 and n2 are selected independently from two non-normally distributed populations, then the sampling distribution of the sample mean difference, a. always normal b. always non-normal c. approximately normal only if n1 and n2 are both larger than or equal to 30 d. approximately normal regardless of n1 and n2 , is ____ 15. Of the last 500 customers entering a supermarket, 50 have purchased a wireless phone. If the relative frequency approach for assigning probabilities is used, the probability that the next customer will purchase a wireless phone is a. 0.20 b. 0.10 c. 0.05 d. None of these choices. ____ 16. Which of the following is a discrete random variable? a. The Dow Jones Industrial average. b. The number of employees of a soft drink company. c. The time it takes you to drive to school. d. The volume of water in Michigan Lakes. ____ 17. It is desired to estimate the average total compensation of CEOs in the publishing industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000). Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000? a. Yes, and I am sure of that. b. Yes, and I am 95% confident of that. c. No, and I am sure of that. d. No, and I am 95% confident of that. ____ 18. In its standardized form, the normal distribution: a. has a mean of 1 and a variance of 0. b. has a mean of 0 and a standard deviation of 1 c. has an area equal to 0.5. d. cannot be used to approximate discrete probability distributions. ____ 19. If X and Y are any random variables with COV(X, Y) = 0.25, correlation is a. 1.417 b. .595 c. 0.351 d. 0.254 , and , then the coefficient of ____ 20. If the mean of an exponential distribution is 2, then the value of the parameter is a. 0.5 b. 2.0 c. 4 d. 1.0 ____ 21. If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is: a. 1.23 b. 0.88 c. 0.47 d. 0.11 ____ 22. The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a x b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. ____ 23. An estimator is said to be consistent if: a. the difference between the estimator and the population parameter grows smaller as the sample size grows larger. b. it is an unbiased estimator. c. the variance of the estimator is zero. d. the difference between the estimator and the population parameter stays the same as the sample size grows larger. ____ 24. A posterior probability value is a prior probability value that has been: a. multiplied by a conditional probability value. b. modified on the basis of new information. c. divided by a conditional probability value. d. added to a conditional probability value. ____ 25. Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if a. np 5 and n(1 p) 5 b. np 5 and np(1 p) 5 c. np 5 and n(1 p) 5 d. None of these choices. ____ 26. The expected value, E(X), of a binomial probability distribution with n trials and probability p of success is: a. n + p b. np(1 p) c. np d. n + p 1 ____ 27. Which of the following conditions does not allow you to use the formula a. Population is normally distributed and the population variance is known. b. Population is not normally distributed but n is large; population variance is known. c. Population has any distribution and n is any size. d. All of these choices allow you to use the formula. to estimate