Question

Problem List Previous Problem Next Problem (4 points) When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as follows: x 12 3456 78 P(X) 0.224 0.128 0.102 0.088 0.064 0.03 0.020.344 A. Mean B. Standard Deviation = The cost of parking is 4.25 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates. A. Mean = B. Standard Deviation

Answer 1

X	P(X)	XP(X)	X^2P(X)
1	0.224	0.224	0.224
2	0.128	0.256	0.512
3	0.102	0.306	0.918
4	0.088	0.352	1.408
5	0.064	0.32	1.6
6	0.03	0.18	1.08
7	0.02	0.14	0.98
8	0.344	2.752	22.016
TOTAL->	1	4.53	28.738

Mean :

$E(X)=\sum X*P(X)=4.53$

Therefore mean parking time is 4.53 hours .

Standard deviation :

$sd=\sqrt{\sum X^2*P(X)-[E(X)]^2}=\sqrt{28.738-(4.53)^2}=2.8665$

Standard deviation of parking time is 2.8665 hours .

Now the cost of parking is 4.25$ per hour

Mean of amount of revenue each car generate = E(X) * 4.25$ = 4.53 * 4.25 =19.2525 $

And

Standard deviation  of amount of revenue each car generate = sd * 4.25$ = 2.8665 * 4.25 =12.1826 $