Question

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	1	2	3	4	5	6	7	8
P(X)	0.213	0.117	0.12	0.085	0.062	0.028	0.023	0.352

A. Mean = _______ 

B. Standard Deviation = _______ 

The cost of parking is 3.25 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)	Mean= X.P(X)	(X-Mx)^2	Variance= P(X).(X-Mx)^2
1	0.213	0.213	12.974404	2.763548052
2	0.117	0.234	6.770404	0.792137268
3	0.12	0.36	2.566404	0.30796848
4	0.085	0.34	0.362404	0.03080434
5	0.062	0.31	0.158404	0.009821048
6	0.028	0.168	1.954404	0.054723312
7	0.023	0.161	5.750404	0.132259292
8	0.352	2.816	11.546404	4.064334208
	Sum of X.P(X), Mx	4.602
	Sum of P(X).(X-Mx)^2, Vx	8.155596
	Standard Deviation	2.855800413

a) Mean, Mx= 4.602

b) SD= sqrt(Vx)= 2.855

3.25 $ per hour

c) Mean revenue= 4.602*3.25= 14.956$

d) SD= 2.855*3.25= 9.278 $

Hope this helps and Please don't forget to rate the answer :)

Answer 2

How did you calculate the standard deviation?