Question

2. When parking a car in a downtown parking lot, drivers pay according to the number of hours or parts thereof. The probability distribution of the number of hours that cars are parked has been estimated as follows:

X                  1        2        3        4        5        6        7        8

P(X)             .24     .18     .13     .10     .07     .04     .04     .20

a. Find the mean and standard deviation of the number of hours that cars are parked in the lot.

b. If the cost of parking is $2.50 per hour, calculate the mean and standard deviation of the amount of revenue each car generates.

Answer 1

a)

b)

E(2.5X)=2.5(E(X))=2.5*(193/50)= 9.65----> MEAN AMOUNT OF REVENUE OF EACH CAR

VAR(2.5X)=2.5^2(VAR(X))=6.25*(2.6039^2)=42.37

THE STD DEV OF AMOUNT OF REVENUE OF EACH CAR GENERATES= =6.5345

SINCE VARIANCE = (STD DEV)^(1/2)