A small accounting firm recently leased a new document management device (an all

Question

A small accounting firm recently leased a new document management device (an all-in-one machine capable of printing, scanning, copying, and faxing) for three years. Reliability was a deciding factor. The company’s research found that during any given year, approximately 86% of the devices sold in one particular model required no service in a year, 9% needed one repair, 4% needed two repairs, 1% required three repairs, and none required more than three repairs in a year. Considering this information to suggest a probability distribution for the number of repairs, find the standard deviation of the number of repairs required in a year. 0.55 repairs. 1.00 repairs. 0.89 repairs. 1.20 repairs. 0.20 repairs.

Explanation / Answer

Let X be the number of repairs in one year

Then

P(X=0) = 0.86

P(X=1) = 0.09

P(X=2) = 0.04

P(X=3) = 0.01

Thus,

E(X) = 0*0.86 + 1*0.09 + 2*0.04 + 3*0.01 = 0.09 + 0.08 + 0.03 = 0.20

E(X2) = 0*0.86 + 1*0.09 + 4*0.04 + 9*0.01 = 0.09 + 0.16 + 0.09 = 0.34

Variance = E(X2) - (E(X) )2 = 0.34 - 0.22 = 0.3

Thus standard deviation = Square root of 0.3 = 0.547

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