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 of the company's annual expense with the service contract for the presentation equipment is ________________________ .
A)$105
B)$10.25
C)$187.42
D)$13.69
E)$2.75

Question

Quizplus · Accepted Answer

The standard deviation of the company's annual expense can be calculated using the probabilities and the costs associated with each outcome. First, calculate the expected value (mean) of the annual expense, then use it to calculate the variance, and finally, take the square root of the variance to find the standard deviation.Expected annual expense (mean) = Probability(No repair) * Cost(No repair) + Probability(1 repair) * Cost(1 repair) + Probability(2 repairs) * Cost(2 repairs) + Probability(3 repairs) * Cost(3 repairs)= 0.86 * ($100) + 0.09 * ($100 + $25*1) + 0.04 * ($100 + $25*2) + 0.01 * ($100 + $25*3)= $86 + $11.25 + $10 + $3.75= $111Variance = Sum(Probability * (Cost - Mean)^2)= 0.86 * ($86 - $111)^2 + 0.09 * ($125 - $111)^2 + 0.04 * ($150 - $111)^2 + 0.01 * ($175 - $111)^2= 0.86 * (-$25)^2 + 0.09 * $14^2 + 0.04 * $39^2 + 0.01 * $64^2= 0.86 * 625 + 0.09 * 196 + 0.04 * 1521 + 0.01 * 4096= 537.5 + 17.64 + 60.84 + 40.96= 656.94Standard deviation = sqrt(Variance)= sqrt(656.94)≈ $25.62However, none of the provided options match the calculated standard deviation. It seems there might have been a mistake in the calculation or in the interpretation of the options. Given the options, none directly match the calculated value, suggesting a need to reevaluate the calculation or the options provided.

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