Exam P Practice Problem 62 – Waiting for Telephone Calls

Problem 62-A

An individual classifies the telephone calls he receives into the categories of Personal Calls (e.g. calls from friends and relatives) and Non-Personal Calls (all the other calls that are considered not Personal Calls).

Let X be the time (in minutes) until the next Personal Call. Let Y be the time (in minutes) until the next Non-Personal Call.

Suppose that X and Y are independent random variables and follow exponential distributions with means 8 minutes and 3 minutes, respectively.

What is the probability that the next incoming telephone call is a Personal Call?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2727

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.3735

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.5000

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.6265

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.7273

\text{ }

\text{ }

\text{ }

\text{ }

Problem 62-B

An individual classifies the telephone calls he receives into the categories of Personal Calls (e.g. calls from friends and relatives), Business Calls (calls related to his small business) and Other Calls (all the other calls not belonging to the Personal Call and Business Call categories).

Let X be the time (in minutes) until the next Personal Call, let Y be the time (in minutes) until the next Business Call and let Z be the time (in minutes) until the next Other Call.

Suppose X, Y and Z are independent random variables and follow exponential distributions with means 12, 10 and 6 minutes, respectively.

What is the probability that the next telephone call this individual receives will be a Business Call?

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3}{14}

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{4}{14}

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{3}

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{5}{14}

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{6}{14}

______________________________________________________

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

\text{ }

______________________________________________________

Answers

______________________________________________________

\copyright \ 2013

Advertisements

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: