d. 36 and 8
____
13. When constructing a confidence interval for the population mean and a small sample is used, the degrees of freedom for the t
distribution equals a. n-1
b. n c. 29 d. 30
_____ 14. The collection of all possible sample points in an experiment is a. the sample space b. a sample point c.an experiment d. the population _____ 15. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there? a. 20 b. 7 c. 5! d. 10 _____ 16. The “Top Three” at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many “Top Three” outcomes are there? a. 302,400 b. 720 c. 1,814,400 d. 10 _____ 17. Given that event E has a probability of 0.25, the probability of the complement of event E a. cannot be determined with the above information b. can have any value between zero and one c. must be 0.75 d. is 0.25 _____ 18. The symbol ? shows the a.union of events b. intersection of events c.sum of the probabilities of events d. sample space _____ 19. If P(A) = 0.38, P(B) = 0.83, and P(A ? B) = 0.57; then P(A ? B) = a. 1.21 b. 0.64 c. 0.78 d. 1.78 _____ 20. If P(A) = 0.62, P(B) = 0.47, and P(A ? B) = 0.88; then P(A ? B) = a. 0.2914 b. 1.9700 c. 0.6700 d. 0.2100 _____ 21. If P(A) = 0.85, P(A ? B) = 0.72, and P(A ? B) = 0.66, then P(B) = a. 0.15 b. 0.53 c. 0.28 d. 0.15 _____ 22. Two events are mutually exclusive if a. the probability of their intersection is 1 b. they have no sample points in common c. the probability of their intersection is 0.5 d. the probability of their intersection is 1 and they have no sample points in common _____ 23. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ? B) = a. 0.30 b. 0.15 c. 0.00 d. 0.20 _____ 24. If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A ? B) = a. 0.00 b. 0.15 c. 0.8 d. 0.2 _____ 25. A subset of a population selected to represent the population is a a.subset b.sample c.small population d. None of the alternative answers is correct. _____ 26. A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have a. the same probability of being selected b. a probability of 1/n of being selected c. a probability of 1/N of being selected d. a probability of N/n of being selected _____ 27. A probability distribution for all possible values of a sample statistic is known as a a.sample statistic b.parameter c.simple random sample d.sampling distribution
_____ 28. From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is a. 3 b. 2 c. greater than 2 d. less than 2 _____ 29. From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately a. 1.1022 b. 2 c. 30 d. 1.4847
Short Answer/Problems
Directions: Clearly designate your solution to each portion of the questions asked and show your entire work and method for arriving at the solution.
1. The sales records of a real estate agency show the following sales over the past 200 days:
# Houses Sold Number of Days 0 60 1 80 2 40 3 16 4 4 a. How many sample points are there?
b. Assign probabilities to the sample points and show their values. c. What is the probability that the agency will not sell any houses in a given day? d. What is the probability of selling at least 2 houses? e. What is the probability of selling 1 or 2 houses? f. What is the probability of selling less than 3 houses?
2. Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4.
a. Find P(A ? B). b. Find P(A ? B). c. Find P(A?B).
3.You are given the following information on Events A, B, C, and D. P(A) = .4, P(B) = .2, P(C) = .1, P(A ? D) = .6, P(A?B) = .3, P(A ? C) = .04, P(A ? D) = .03
a. Compute P(D). b. Compute P(A ? B). c. Compute P(A?C). d. Compute the probability of the complement of C. e. Are A and B mutually exclusive? Explain your answer. f. Are A and B independent? Explain your answer. g. Are A and C mutually exclusive? Explain your answer. h. Are A and C independent? Explain your answer.
4. Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces.
a. Determine the mean and the variance of the population. b. Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of . c. Compute the standard error of the mean.
5. A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b. What is the probability that these 64 students will spend a combined total of more than $715.21? c. What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?
Solutions to MC Problems 1. ANS: B2ANS:C3.ANS:C4. 11. ANS: A12.ANS:C13.ANS: 19. ANS: B20.ANS:D21.ANS: 27. ANS: D28.ANS: D
ANS:A5. ANS:C6. ANS:B7.ANS:D 8.ANS:C9.ANS:B10.
A14.ANS:A15.ANS: D16.ANS:B17.ANS: C18.ANS:AB22.ANS:B23.ANS:C24.ANS:C25. ANS: B26. ANS:
ANS:AA
29. ANS: D
Short Answer/Problems
Directions: Clearly designate your solution to each portion of the questions asked and show your entire work and method for arriving at the solution.
1. ANSWERS: a. 5 b. Houses Sold Probability 0 0.30 1 0.40 2 0.20 3 0.08 4 0.02 c. 0.3d. 0.3e. 0.6f. 0.9 2. ANSWERS:a. 0.0 b. 0.6 c. 0.0 3ANSWERS:
a. g.
0.23b. 0.06c. 0.4d. 0.9e. No, P(A?B) ? 0f. No, P(A?B) ? P(A) No, P(A ? C) ? 0h. Yes, P(A?C) = P(A)
4. ANSWERS:a. 5 and 8b. 5. ANSWERS:a. 10.5 0.363
5 and 3c. 1.732
normalb.0.0314c. 0.0794