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The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass.gov website, November 2012). Suppose the number of calls per hour follows a Poisson probability distribution. a. What is the mean time between 911 calls to the Boston Fire Department in minutes? b. Using the mean in part (a), show the probability density function for the time between 911 calls in minutes. c. What is the probability that there will be less than one hour between 911 calls? d. What is the probability that there will be 30 minutes or more between 911 calls? e. What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 6.4, Problem 38E
Textbook Problem
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The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass.gov website, November 2012). Suppose the number of calls per hour follows a Poisson probability distribution.

  1. a. What is the mean time between 911 calls to the Boston Fire Department in minutes?
  2. b. Using the mean in part (a), show the probability density function for the time between 911 calls in minutes.
  3. c. What is the probability that there will be less than one hour between 911 calls?
  4. d. What is the probability that there will be 30 minutes or more between 911 calls?
  5. e. What is the probability that there will be more than 5 minutes, but less than 20 minutes between 911 calls?

a.

To determine

Find the mean time between the 911 calls in minutes.

Explanation of Solution

Calculation:

The department of Boston fire gets 911 calls with a mean rate of 1.6 calls per hour. The number of calls per hour follows Poisson distribution.

The number of calls follows Poisson distribution but the time between calls follows the exponential distribution.

The mean time between 911 calls is,

μ=<

b.

To determine

Find the probability density function for time between 911 calls.

c.

To determine

Find the probability that the time between 911 calls will be less than one hour.

d.

To determine

Find the probability that the time between 911 calls will be more than or equal to 30 minutes.

e.

To determine

Find the probability that the time between 911 calls will be less than 20 minutes but more than 5 minutes.

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Chapter 6 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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