Question

An attendant at a car wash is paid according to the number of cars that pass through. Suppose that following payments are made with the following probabilities: Payment Probability $7 0.18 $9 0.08 $11 0.09 $13 0.16 $15 0.08 $17 0.41 Find the standard deviation of the attendant's earnings.

Answer 1

`E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22`

And we can find the second moment with this formula:

`E(X^2) = \sum_(i=1)^n X^2_i P(X_i)`

And replacing we got:

`E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72`

And we can find the variance like this:

`Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516`

And the deviation would be:

`Sd(X)= √(14.9516)= 3.867`

Explanation:

For this case we have the following dataset given:

Payment $7 $9 $11 $13 $15 $17

Probability 0.18 0.08 0.09 0.16 0.08 0.41

For this case we can calculate the mean with this formula:

`E(X) = \sum_(i=1)^n X_i P(X_i)`

And replacing we got:

`E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22`

And we can find the second moment with this formula:

`E(X^2) = \sum_(i=1)^n X^2_i P(X_i)`

And replacing we got:

`E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72`

And we can find the variance like this:

`Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516`

And the deviation would be:

`Sd(X)= √(14.9516)= 3.867`