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...

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.

Asked on by jenny321

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

aznboy578's profile pic

aznboy578 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

mean revenue for the probability distribution= $9.65

standard deviation of the revenue earned = $6.5098

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