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# A traffic light at a certain intersection is green 50% of ISBN: 9780073401331 38

## Solution for problem 4E Chapter 4.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

A traffic light at a certain intersection is green 50% of the time, yellow 10% of the time, and red 40% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.

a. Find P(X = 3).

b. Find P(X<3).

c. Find μX

d. Find Step-by-Step Solution:

Step 1 of 5:

Given,  at a certain intersection of a traffic light, green is 50%  of the time, yellow is 10% of the time and red is 40% of the time.

Let X = number of days that pass up to and including the first time the car encounters a red light.

Assumption is that each day represents an independent trial.

Let X follows Geometric distribution and probability mass function of the Geometric distribution is

P(x)  =  p  (1 - p , x = 1, 2, …..

Where, p = 0.40

Step 2 of 5:

The claim is to find the P(x = 3)

Then, P( x=3 ) = (0.4) (1 - 0.4 = (0.4) (0.6 = (0.4) (0.36)

= 0.144

Hence, P(x = 3) = 0.144

Step 3 of 5:

The claim is to find the P(x < 3)

Then, P( x<3 ) = P(x=1) + P(x=2)

= (0.4) (1 - 0.4 +(0.4) (1 - 0.4 = (0.4) (0.6 + (0.4) (0.6 = (0.4) (1) + (0.4) (0.6)

= 0.4 + 0.24

Hence, P(x <  3) = 0.64

Step 4 of 5

Step 5 of 5

##### ISBN: 9780073401331

This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “A traffic light at a certain intersection is green 50% of the time, yellow 10% of the time, and red 40% of the time. A car approaches this intersection once each day. Let X represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.a. Find P(X = 3).________________b. Find P(X<3).________________c. Find ?X________________d. Find” is broken down into a number of easy to follow steps, and 71 words. Since the solution to 4E from 4.4 chapter was answered, more than 1228 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: Find, day, Car, red, light. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 4E from chapter: 4.4 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM.

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