A consumer products magazine indicated that the average life

A consumer products magazine indicated that the average life of a refrigerator before replacement is

= 13 years with a (95% of data) range from 7 to 19 years. 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.Estimating the standard deviation

For a symmetric, bell-shaped distribution,

where it is estimated that about 95% of the commonly occurring data values fall into this range. Use this \"rule of thumb\" to approximate the standard deviation of x values. (Round your answer to one decimal place.)
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(b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? (Round your answer to four decimal places.)


(c) What is the probability that someone will keep a refrigerator more than 18 years before replacement? (Round your answer to four decimal places.)


(d) 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 9% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)?
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Solution