Practice Questions Chapter 4 & 5

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1 Practice Questions Chapter 4 & 5 Use the following to answer questions 1-3: Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to What is the probability that the next three babies are of the same sex? A) B) C) D) Define event B = {at least one of the next two babies is a boy}. What is the probability of the complement of event B? A) B) C) D) What is the probability that at least one of the next three babies is a boy? A) B) C) D) A valid probability is any number between 1 and 1. A) True B) False 5. In a probability model, all possible outcomes together must have a probability of 1? A) True B) False 6. If two events have no outcomes in common, then those two events are. A) independent B) disjoint Page 1

2 7. Two events are considered independent if the outcome of one does not influence the outcome of the other? A) True B) False 8. You decide to visit the health center to be tested for HIV, the virus that causes AIDS. What is the sample space that represents your possible result? 9. Binomial distributions represent random variables. A) discrete B) continuous C) None of the above. 10. Normal distributions represent random variables. A) discrete B) continuous C) None of the above. Use the following to answer questions 11-16: The probability distribution of random variable, X, is defined as follows: X Probability Is the above a valid probability model? A) Yes B) No 12. The table above describes a random variable that is. A) discrete B) continuous C) both discrete and continuous D) None of the above. 13. The expected value of the probability distribution is. 14. The P(X = 0) = Page 2

3 15. The P(X < 4) = 16. The P(X > 0) = Use the following to answer question 17: Consider the following probability histogram for a discrete random variable X: 17. What is P(X < 3)? A) 0.10 B) 0.25 C) 0.35 D) 0.65 Use the following to answer questions 18-20: The probability density of a continuous random variable X is given in the figure below: Page 3

4 18. Based on this density, what is the probability that X is between 0.5 and 1.5? A) 1 3 B) 1 2 C) 3 4 D) What is the P(X = 1.5)? A) 0 B) 1 4 C) ⅓ D) What is the P(X 1.5)? A) 0 B) 1 4 C) ⅓ D) 1 2 Use the following to answer questions 21-23: The weight of medium-size tomatoes selected at random from a bin at the local supermarket is a random variable with mean = 10 oz and standard deviation = 1 oz 21. Suppose we pick four tomatoes from the bin at random and put them in a bag. Define the random variable Y = the weight of the bag containing the four tomatoes. What is the mean of the random variable Y? A) Y = 2.5 oz B) Y = 4 oz C) Y = 10 oz D) Y = 40 oz 22. Suppose we pick four tomatoes from the bin at random and put them in a bag. Define the random variable Y = the weight of the bag containing the four tomatoes. What is the standard deviation of the random variable Y? A) Y = 0.50 oz B) Y = 1.0 oz C) Y = 2.0 oz D) Y = 4.0 oz Page 4

5 23. Suppose we pick two tomatoes at random from the bin. Let the random variable V = the difference in the weights of the two tomatoes selected (the weight of the first tomato minus the weight of the second tomato). What is the standard deviation of the random variable V? A) V = 0.00 oz B) V = 1.00 oz C) V = 1.41 oz D) V = 2.00 oz Use the following to answer questions 24-27: The table below shows the political affiliation of 1000 randomly selected American voters and their positions on the school of choice program: Political party Position Democrat Republican Other Favor Oppose Let the event D = {voter is a Democrat}, R = {voter is a Republican}, and F = {voter favors the school of choice program}. For each of the following questions, write the probability in symbols (e.g., P(D)) and calculate the probability. 24. What is the probability that a randomly selected voter favors the school of choice program? A) P(F) = 0.30 B) P(F) = 0.36 C) P(F) = 0.38 D) P(F) = What is the probability that a randomly selected Republican favors the school of choice program? A) P(F R) = 0.12 B) P(R F) = 0.19 C) P(F R) = 0.33 D) P(R F) = 0.36 Page 5

6 26. What is the probability that a randomly selected voter who favors the school of choice program is a Democrat? A) P(D F) = 0.26 B) P(D F) = 0.42 C) P(F D) = 0.48 D) P(F D) = A candidate thinks she has a good chance of gaining the votes of anyone who is a Democrat or who is in favor of the school of choice program. What proportion of the 1000 voters is that? A) P(D or F) = 0.26 B) P(D and F) = 0.65 C) P(D or F) = 0.66 D) P(D F) = Suppose a simple random sample is selected from a population with mean and variance 2. The central limit theorem tells us that A) the sample mean x gets closer to the population mean as the sample size increases. B) if the sample size n is sufficiently large, the sample will be approximately Normal. C) the mean of x will be if the sample size n is sufficiently large. D) if the sample size is sufficiently large, the distribution of x will be approximately Normal with mean and standard deviation, n. E) the distribution of x will be Normal only if the population from which the sample is selected is also Normal. Use the following to answer question 29: Let X represent the SAT score of an entering freshman at University X. The random variable X is known to have a N(1200, 90) distribution. Let Y represent the SAT score of an entering freshman at University Y. The random variable Y is known to have a N(1215, 110) distribution. A random sample of 100 freshmen is obtained from each university. Let X = the sample mean of the 100 scores from University X, and Y = the sample mean of the 100 scores from University Y. Page 6

7 29. What is the distribution of the difference in sample means between University X and University Y: X Y? A) N( 15, 20) B) N( 15, 14.2) C) N( 15, 142.1) D) N( 15, 200) Use the following to answer questions 30-31: A population variable has a distribution with mean = 50 and variance 2 = 225. From this population a simple random sample of n observations is to be selected and the mean x of the sample values calculated. 30. How big must the sample size n be so that the standard deviation of the sample mean, x, is equal to 1.4, i.e., x = 1.4? A) n = 11 B) n = 161 C) n = 115 D) n = 36 E) n = If the population variable is known to be Normally distributed and the sample size used is to be n = 16, what is the probability that the sample mean will be between and 55.74, i.e., P(48.35 x 55.74)? A) B) C) D) E) Not within ± of any of the above. Page 7

8 Answer Key 1. B 2. B 3. D 4. B 5. A 6. B 7. A 8. S = {Positive for HIV, Negative for HIV} 9. A 10. B 11. A 12. A C 18. B 19. A 20. B 21. D 22. C 23. C 24. D 25. C 26. B 27. C 28. D 29. B 30. C 31. B Page 8

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