5.63 Traffic Fatalities and Intoxication. The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic fatality will involve an intoxicated or alcohol- impaired driver or nonoccupant. In eight traffic fatalities, find the probability that the number, Y, that involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y.5.88 Motel Reservations. M. F. Driscoll and N. A. Weiss dis- cussed the modeling and solution of problems concerning mo- tel reservation networks in \"An Application of Queuing Theory to Reservation Networks\" (TIMS, Vol. 22, No. 5, pp. 540546). They dened a Type 1 call to be a call from a motel's computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribu- tion with parameter = 1.7. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be a. exactly one. b. at most two. (3. at least two. (Hint: Use the complementation rule.) (1. Find and interpret the mean of the random variable X. e. Determine the standard deviation of X. 5.3 Let X denote the number of siblings of a randomly selected student. Explain the difference between {X = 3} and P (X = 3). 5.7 Space Shuttles. The National Aeronautics and Space Ad- ministration (NASA) compiles data on space-shuttle launches 218 CHAPTER 5 Discrete Random Variables* and publishes them on its Web site. The following table displays a frequency distribution for the number of crew members on each shuttle mission from April 1981 to July 2000. Crewsize2345678 Frequency 4 l 2 36 18 33 2 Let X denote the crew size of a randomly selected shuttle mission between April 1981 and July 2000. a. What are the possible values of the random variable X? b. Use random-variable notation to represent the event that the shuttle mission obtained has a crew size of 7. c. Find P(X = 4); interpret in terms of percentages. d. Obtain the probability distribution of X. e. Construct a probability histogram for X. 3. Identify the possible values of the random variable X. b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the rst born is a girl and the next three born are boys.) Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability dis- tribution obtained in part (b) to determine each event's probabil- ity. The couple has 1:. exactly two girls. (1. at least two girls. e. at most two girls. 1'. between one and three girls, inclusive. g. children all of the same gender. 5.11 Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 147. Let Y denote the sum of the dice