Question

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation

Answer 1

X denotes the time needed to change the oil on a car, which follows a uniform distribution between 11 and 21 minutes. The probability of X being greater than 19 is 0.2.

Step-by-step explanation:

a. X is the time needed to change the oil on a car.

b. X follows a uniform distribution between 11 and 21 minutes.

c. The distribution is a rectangular shape with height 1/10 and width 10 (from 11 to 21 minutes).

d. To find P(x > 19), we need to calculate the probability of X being greater than 19. Since X follows a uniform distribution, the probability can be found by dividing the length of the interval greater than 19 by the total length of the interval. In this case, the length of the interval greater than 19 is 21 - 19 = 2, and the total length of the interval is 21 - 11 = 10. Therefore, P(x > 19) = 2/10 = 1/5 = 0.2.