# Exam P Practice Problem 35 – Lifetime of Machine

Problem 35A

The lifetime (in years) of a manufacturing equipment follows a distribution with the following probability density function:

$\displaystyle f(t)=\frac{1}{10 \ \sqrt{t}} \ \ e^{\displaystyle -\frac{\sqrt{t}}{5}} \ \ \ \ \ \ \ 0

A factory owner just bought such an equipment that is 5-year old and is in working condition. What is the probability that it will work for another 5 years?

$\displaystyle A \ \ \ \ \ \ 0.5313$

$\displaystyle B \ \ \ \ \ \ 0.5875$

$\displaystyle C \ \ \ \ \ \ 0.6394$

$\displaystyle D \ \ \ \ \ \ 0.8310$

$\displaystyle E \ \ \ \ \ \ 0.9043$

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Problem 35B

The time (in weeks) it takes a home builder to build a house follows a continuous distribution with the following density function:

$\displaystyle f(t)=\frac{3}{32} \ \ t \ (4-t) \ \ \ \ \ \ \ 0

A customer signs a contract to hire this home builder to build a house. The construction begins immediately after the signing of the contract.

Two weeks into the contract, the customer finds that the house is not completed. What is the probability that the total time from start to completion is three weeks or less?

$\displaystyle A \ \ \ \ \ \ \frac{11}{32}$

$\displaystyle B \ \ \ \ \ \ \frac{16}{32}$

$\displaystyle C \ \ \ \ \ \ \frac{22}{32}$

$\displaystyle D \ \ \ \ \ \ \frac{24}{32}$

$\displaystyle E \ \ \ \ \ \ \frac{27}{32}$

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