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<t<\infty

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

\text{ }

\text{ }

\text{ }

\text{ }

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<t<4

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}

__________________________________________________________________

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

__________________________________________________________________

Answers

__________________________________________________________________

\copyright \ 2013

Advertisements

One response

  1. Why does the exponential memory-less property not work for 35A after a change of variable sqrt (t) = u and survival rate function bounded over sqrt (5) units ? It does not yield the same answer as conditioning on machine having survived sqrt (5) units already.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: