A consumer products magazine indicated that the average life of a refrigerator b

Question

A consumer products magazine indicated that the average life of a refrigerator before replacement is = 13 years with a (95% of data) range from 9 to 17years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal.

(a) The empirical rule indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from – 2 to + 2 is often used for "commonly occurring" data values. Note that the interval from – 2 to + 2 is 4 in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values.

1) Assume that the average life of a refrigerator is 13 years, with the standard deviation given in part (a) before it breaks. Suppose that a company guarantees refrigerators and will replace a refrigerator that breaks while under guarantee with a new one. However, the company does not want to replace more than 10% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?

Explanation / Answer

a)

95% data is between 2* standard deviation

=>

mean + 2 * std = 17

=>

standard deviation = 17 - 13 / 2 = 2

b)

P(X < x) = 0.1

=>

P(Z < x -13/2) = 0.1

=>

x -13 / 2 = invnorm(0.1)

=>

x-13 / 2 = -1.282

=>

x = 10.4 years

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