Homework SourseWhen parking a car in a downtown parking lot drivers pay acc
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:
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 =
| X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P(X) | 0.218 | 0.135 | 0.124 | 0.084 | 0.058 | 0.03 | 0.031 | 0.32 |
Solution
A. Mean =E(X)=x*f(x)= 1*0.218+2*0.135+3*0.124+4*0.084+5*0.058+6*0.03+7*0.031+8*0.32 = 4.443
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E(X^2) =1*0.218+2^2*0.135+3^2*0.124+4^2*0.084+5^2*0.058+6^2*0.03+7^2*0.031+8^2*0.32 = 27.747
Variance= E(X^2) - [E(X)]^2 = 27.747- 4.443^2= 8.006751
B. Standard Deviation = sqrt(8.006751) = 2.82962
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A. Mean =3.25*4.443 = 14.43975
B. Standard Deviation =3.25*2.82962 = 9.196265
