Suppose that the average life of a refrigerator before replacement is $mu$ = 15 years with a (68% of data) range from 13 to 17 years. Let x = age at which a refrigerator is replaced. Assume that x has a distribution that is approximately normal. Find a good approximation for the standard deviation of x values. 3 years • 5 years 6 years 2 years 1 year
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Step 1: Given that the average life of a refrigerator before replacement is 15 years with a range from 13 to 17 years (68% of data), we can determine the standard deviation using the formula for a normal distribution. Show more…
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8. The average life of a refrigerator has a normal distribution with mean 14 years and standard deviation σ years. (a) If 95% of fridges last between 9 and 19 years, show that σ = 2.55 (3 s.f.). (b) What is the probability a fridge lasts less than 11 years? (c) A company guarantees fridges and will replace a refrigerator which breaks while under guarantee with a new one. The company does not want to replace more than 5% of fridges. For how long should the guarantee be made?
Joanna Q.
the lifespans of refrigerators are normally distributed with the mean of 14 years and standard deviation of 2.5 years. using the empirical rule, 68% of refrigerators have a lifespan between what two years
Steven C.
Refrigerator Replacement Consumer Reports indicated that the average life of a refrigerator before replacement is $\mu=14$ years with a $(95 \% \text { of data) range from } 9 \text { to } 19 \text { years. Let } x=$ age at which a refrigerator is replaced. Assume that $x$ has a distribution that is approximately normal. (a) Find a good approximation for the standard deviation of $x$ values. Hint: See Problem 31. (b) What is the probability that someone will keep a refrigerator fewer than 11 years before replacement? (c) What is the probability that someone will keep a refrigerator more than 18 years before replacement? (d) Inverse Normal Distribution Assume that the average life of a refrigerator is 14 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 $5 \%$ 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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