A small business just leased a new computer and color laser

A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The company’s research suggested that during a given year 86% of these computers needed no repairs, 9% needed to be repaired once, 4% twice, 1% three times, and none required more than three repairs.

Find the expected number of repairs this computer needs each year.

1       b. 0.86       c. 2       d. 0.04       e. 0.20

The standard deviation of the number of repairs each year is 0.55. What is the standard deviation ofthe company\'s annual expense for the service contract?

$13.75       b. $113.75       c. $55.00       d. $38.75       e. $125.00

Solution

a)
E(x)= 0*0.86 + 1*0.09 + 2*0.04 + 3*0.01 = 0.2
b)

E[annual expense] = 100(.86) + 125(.09) + 150(.04) + 175(.01) = 105
E[(annual expense)^2] = 100^2(.86) +125^2(.09) + 150^2(.04) + 175^2(.01) = 11212.5
Var[A] = E[A^2] -[E[A]]^2
Var[A] = 11212.5 - 105^2 = 187.5
SD[A] = Sqrt( Var[A] ) = Sqrt(187.5) = 13.69 [ Nearest Answer be $13.75 ]