Name: Date: Pd: Quiz Review

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1 Name: Date: Pd: Quiz Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A die is cast repeatedly until a 1 falls uppermost. Let the random variable X denote the number of times the die is cast. What are the values that X may assume? a. X may assume the values in the set S = {1, 2, 3,...} b. X may assume the values in the set S = {1} c. X may assume the values in the set S = {1, 2, 3, 4, 5, 6} 2. Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of times a die is thrown until a 1 appears. a. X may assume the values of any positive integer. The random variable is finite discrete. b. X may assume the values of any positive integer. The random variable is continuous. c. X may assume the values in the set S = {1, 2, 3, 4, 5, 6}. The random variable is finite discrete. d. X may assume the values of any positive integer. The random variable is infinite discrete. 3. The histograms represent the probability distributions of the random variables X and Y. Determine by inspection which probability distribution has the larger variance. a. a b. b 4. Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The distance a commuter travels to work a. { }. The random variable is infinite discrete. b. { }. The random variable is continuous. c. { }. The random variable is finite discrete.

2 Short Answer 5. An examination consisting of ten true-or-false questions was taken by a class of 100 students. The probability distribution of the random variable X, where X denotes the number of questions answered correctly by a randomly chosen student, is represented by the accompanying histogram. The rectangle with base centered on the number 8 is missing. What should be the height of this rectangle? 6. In a lottery, 7,000 tickets are sold for $1 each. One first prize of $3,500, 1 second prize of $700, 3 third prizes of $210, and 10 consolation prizes of $35 are to be awarded. What are the expected net earnings of a person who buys one ticket? 7. During the first year at a university that uses a 4-point grading system, a freshman took ten 3-credit courses and received one A, three Bs, two Cs, and four Ds. Compute this student's grade point average. 8. Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 DVDs. How many DVDs can a customer entering this store be expected to buy? DVDs Probability

3 9. Steffi feels that the odds in favor of her winning her tennis match tomorrow are 1 to 11. What is the (subjective) probability that she will win her match tomorrow? 10. Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 3 ). 11. Determine whether the table gives the probability distribution of the random variable X. Explain your answer. 12. The minimum age requirement for a regular driver's license differs from state to state. The frequency distribution for this age requirement in the 50 states is: Minimum Age Frequency of occurrence Compute the mean, variance, and standard deviation of the random variable X. 13. A probability distribution has a mean of 50 and a standard deviation of 1.5. Use Chebychev's inequality to find the value of c that guarantees that the probability is at least 93.75% that an outcome of the experiment lies between 50 - c and 50 + c.

4 14. The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.2, the estimated profit over the next 10 yr is $8 million; if the company obtains the rights to city B, the probability of which is 0.4, the estimated profit over the next 10 yr is $9 million. The cost of submitting a bid for rights in city A is $150,000 and that of city B is $250,000. By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B. 15. The accompanying data were obtained in a study conducted by the manager of one supermarket. In this study the number of customers waiting in line at the express checkout at the beginning of each 3-min interval between 9 A.M. and 12 noon on Saturday was observed. Customers Frequency of Occurrence Find the probability distribution of the random variable X, where X denotes the number of customers observed waiting in line. Draw the histogram representing the probability distribution.

5 Quiz Review 8.1 & 8.2 Answer Section MULTIPLE CHOICE 1. A 2. D 3. A 4. B SHORT ANSWER $ E = No, the probability assigned to a value of the random variable cannot be negative. 12. μ = 17.46, Var(X) = , σ = c = City B 15. x P(X = x) x P(X = x)