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# A commuter encounters four traffic lights each day on her

ISBN: 9780073401331 38

## Solution for problem 3E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 3E

A commuter encounters four traffic lights each day on her way to work. Let X represent the number of these that are red lights. The probability mass function of X is as follows.

What is the probability that in a period of 100 days, the average number of red lights encountered is more than 2 per day?

Step-by-Step Solution:

Step 1 of 1:

(a)

In this question, we are asked to find the probability that in a period of  days, the average number of red lights encountered is more than  per day.

A commuter encounters traffic lights each day.

Let  represent the number of these that are red lights.

The probability mass function (PMF) of  is as follows.

 0 1 2 3 4 0.1 0.3 0.3 0.2 0.1

when  is a discrete random variable with probability mass function then we can write

= .The mean of  is given by

=  …………(1)

where the sum is for all possible values of .

The variance is given by the following formula

………….(2)

Hence mean number of red lights encountered per day will be

=

=

The standard deviation is

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

The full step-by-step solution to problem: 3E from chapter: 4.11 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “A commuter encounters four traffic lights each day on her way to work. Let X represent the number of these that are red lights. The probability mass function of X is as follows. What is the probability that in a period of 100 days, the average number of red lights encountered is more than 2 per day?” is broken down into a number of easy to follow steps, and 57 words. This full solution covers the following key subjects: lights, day, red, Probability, average. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 3E from 4.11 chapter was answered, more than 1323 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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A commuter encounters four traffic lights each day on her

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