Question

a.) Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable X as the number of ticketed passengers who actually show up for the flight. The probability function of X is in the accompanying table.

?? 45 46 47 48 49 50 51 52 53 54 55

?(? = ??) .05 .10 .12 .14 .25 .17 .06 .05 .03 .02 .01

1.) What is the probability that the flight will accommodate all ticketed passengers who show up? Show Work

2.) If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight?   Show Work



b.) An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose the probability distribution of X is as follows:

?? 13.5 15.9 19.1

?(? = ??) 0.2 0.5 0.3

Find the expected value of X. Show Work.


c.) Suppose that only 30% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that, of 8 randomly chosen drivers coming to an intersection under these conditions, exactly 4 will come to a complete stop?   Answer this question without using R or a binomial calculator function. I want you to simplify the combination manually, but a calculator can certainly be used to multiply the combination by ?? ∙(?−?)?−?. Show Work.

Answer 1