# Exam P Practice Problem 52 – Reliability of Refrigerators

Problem 52-A

The time from initial purchase to the time of the first major repair (in years) for a brand of refrigerators is modeled by the random variable $Y=e^X$ where $X$ is normally distributed with mean 1.2 and variance 2.25.

A customer just bought a brand new refrigerator of this particular brand. The refrigerator came with a two-year warranty. During the warranty period, any repairs, both minor and major, are the responsibilities of the manufacturer.

What is the probability that the newly purchased refrigerator will not require major repairs during the warranty period?

$\displaystyle (A) \ \ \ \ \ \ \ \ 0.2451$

$\displaystyle (B) \ \ \ \ \ \ \ \ 0.2981$

$\displaystyle (C) \ \ \ \ \ \ \ \ 0.3669$

$\displaystyle (D) \ \ \ \ \ \ \ \ 0.6331$

$\displaystyle (E) \ \ \ \ \ \ \ \ 0.7549$

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Problem 52-B

The time from initial purchase to the time of the first major repair (in years) for a brand of refrigerators is modeled by the random variable $Y=e^X$ where $X$ is normally distributed with mean 0.8 and standard deviation 1.5.

What is the median length of time (from initial purchase) that is free of any need for major repairs?

$\displaystyle (A) \ \ \ \ \ \ \ \ 0.80 \text{ years}$

$\displaystyle (B) \ \ \ \ \ \ \ \ 2.23 \text{ years}$

$\displaystyle (C) \ \ \ \ \ \ \ \ 3.50 \text{ years}$

$\displaystyle (D) \ \ \ \ \ \ \ \ 4.71 \text{ years}$

$\displaystyle (E) \ \ \ \ \ \ \ \ 6.86 \text{ years}$

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