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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 5.6, Problem 51E

Textbook Problem

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Over 500 million tweets are sent per day (*Digital Marketing Ramblings* website, December 15, 2014). Assume that the number of tweets per hour follows a Poisson distribution and that Bob receives on average 7 tweets during his lunch hour.

- a. What is the probability that Bob receives no tweets during his lunch hour?
- b. What is the probability that Bob receives at least 4 tweets during his lunch hour?
- c. What is the expected number of tweets Bob receives during the first 30 minutes of his lunch hour?
- d. What is the probability that Bob receives no tweets during the first 30 minutes of his lunch hour?

**a.**

To determine

Compute the probability that Bob receives no tweets during lunch hour.

**Calculation:**

The assumption made is that the number of tweets per hour follows Poisson distribution and that Bob receives on average 7 tweets during his lunch hour.

The Poisson probability function is,

Where, *x* is the number occurrences of the event in a given interval, *e* is a constant that has value 2.71828.

The required probability is the probability at the point

**b.**

To determine

Compute the probability that Bob receives at least 4 tweets during his lunch hour.

**c.**

To determine

Compute the expected number of tweets Bob receives during the first 30 minutes of his lunch hour.

**d.**

To determine

Compute the probability that Bob receives no tweets during the first 30 minutes of his lunch hour.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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