A small business just leased a new presentation equipment and a 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
Indicates that during a given year 86% of these computers need no repairs, 9% need to be
Repaired once, 4% twice, 1% three times, and none required more than three repairs.
The standard deviation in the number of repairs for this kind of computer per year is
A) 0.20 repairs.
B) 0.55 repairs.
C) 0.89 repairs.
D) 1.00 repairs.
E) 1.20 repairs.

Question

Quizplus · Accepted Answer

The expected value of the number of repairs can be calculated as follows:
E(X) = (0.86 x 0) + (0.09 x 1) + (0.04 x 2) + (0.01 x 3) = 0.22
The variance can be calculated as follows:
Var(X) = (0.86 x (0-0.22)^2) + (0.09 x (1-0.22)^2) + (0.04 x (2-0.22)^2) + (0.01 x (3-0.22)^2) = 0.3536
The standard deviation is the square root of the variance:
SD = sqrt(0.3536) = 0.5943 ≈ 0.55
Therefore, the best choice is B.

A Small Business Just Leased a New Presentation Equipment and a Color