Question

Calculate the mean and standard deviatio of he amount of revenue each car generates.When parking a car in a downtown parking lot, drivers pay according tothe number of hours or parts 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) .24 .18 .13 .10 .07 .04 .04 .20
 
The cost of parking is $2.50 per hour.

Accepted Answer

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) .24  .18  .13   .10  .07  .04  .04  .20
The mean is equal to:
1*0.24 + 2*0.18 + 3*0.13 + 4*0.1 + 5*0.07 + 6*0.04 + 7*0.04 + 8*0.2 = 3.86
The standard deviation is:
sqrt((1^2*0.24 + 2^2*0.18 + 3^2*0.13 + 4^2*0.1 + 5^2*0.07 + 6^2*0.04 + 7^2*0.04 + 8^2*0.2) - 3.86^2)
=> sqrt((1*0.24 + 4*0.18 + 9*0.13 + 16*0.1 + 25*0.07 + 36*0.04 + 49*0.04 + 64*0.2) - 3.86^2)
=> sqrt(21.68 - 14.8996)
=> sqrt(6.7804)
=> 2.60392
The revenue earned when the car is parked for an hour is $2.5.
The mean revenue earned is equal to 3.86*2.5 = $9.65 and the standard deviation of the revenue earned is $6.5098
The mean revenue earned for the probability distribution given is $9.65 and the standard deviation of the revenue earned is approximately $6.5098

Answer

mean revenue for the probability distribution= $9.65
standard deviation of the revenue earned = $6.5098

Math

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