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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?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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Chapter
Section
BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

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.

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

Explanation of Solution

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,

f(x)=μxeμx!

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

The required probability is the probability at the point x=0. Substituting the values μ as 7, e as 2

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.

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