When parking a car in a downtown parking lot, drivers pay according to the numbe
ID: 3258367 • Letter: W
Question
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 cars are parked has been estimated as follows. The cost of parking is $2.50 per hour plus a five dollar flat rate.
x | 1 2 3 4 5 6 7 8
----------------------------------------------------------------------------------------
p(x) | 0.24 0.18 0.13 0.10 0.07 0.04 0.04 0.20
Calculate the mean amount of revenue that each car generates. Round to two decimals. Units are in dollars.
Calculate the variance of the amount of revenue that each car generates. Round to two decimals. Units are in dollars squared.
Explanation / Answer
x
p (x)
1
0.24
2
0.18
3
0.13
4
0.1
5
0.07
6
0.04
7
0.04
8
0.2
Mean = sum of x * p (x)
x
p (x)
x *p(x)
1
0.24
0.24
2
0.18
0.36
3
0.13
0.39
4
0.1
0.4
5
0.07
0.35
6
0.04
0.24
7
0.04
0.28
8
0.2
1.6
Total =
3.86
Mean = 3.86
x
p (x)
x *p(x)
x^2*p(x)
1
0.24
0.24
0.24
2
0.18
0.36
0.72
3
0.13
0.39
1.17
4
0.1
0.4
1.6
5
0.07
0.35
1.75
6
0.04
0.24
1.44
7
0.04
0.28
1.96
8
0.2
1.6
12.8
Total =
3.86
21.68
Variance = E(x^2 ) – [ E (x)]^2
= 21.68 – (3.86*3.86)
= 6.78
Variance = 6.78
x
p (x)
1
0.24
2
0.18
3
0.13
4
0.1
5
0.07
6
0.04
7
0.04
8
0.2
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