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

Answer:

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

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:

$Sd(X)= \sqrt{14.9516}= 3.867$

Step-by-step 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:

$Sd(X)= \sqrt{14.9516}= 3.867$