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Refer to Example 4.14. Estimate the probability that

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 25E Chapter 4.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 25E

Refer to Example 4.14. Estimate the probability that exactly one of the four tires has a flaw, and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 25E

Step1 of 3:

Let us consider a random variable X it presents the number of tires out of four that have no flaw.

Also from Example 4.14 we have sample proportion and standard deviation  Let “q” be the probability that exactly one of four tires has a flaw.

Then X follows binomial distribution with parameters “n and p” that is X B(n, p),

The probability mass function of binomial distribution is given by

, x = 0,1,2,...,n.

Where,

n = sample size

   = 4

x = random variable

p = probability of success

q = 1 - p (probability of failure)

We need to Estimate the probability that exactly one of the four tires has a flaw, and also we need to find the uncertainty in the estimate.


Step2 of 3:

Consider,

         

Let q = P(X = 3)

Now,

 

                   =

            = 4

          = 4-4

Estimate of q is and it is given by

     

                         = 4 - 4

                           = 4(0.8043) - 4(0.7480)

                 = 3.2172 - 2.9920

= 0.2252

Hence = 0.2252.


Step3 of 3:

Consider,

     

Differentiate above equation with respect “” we get

         

           = 12-16

                            = 12

                              = 12(0.8649) - 16(0.8043)

                     = 10.3788 - 12.8688

= -2.49

Hence, = -2.49

Therefore, the uncertainty in the estimate is given by

              =

          = (2.49)0.0255

 = 0.0634

Hence the probability is 0.22520.0634.


Step 2 of 3

Chapter 4.2, Problem 25E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 25E from chapter: 4.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: estimate, flaw, Example, Find, exactly. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 25E from 4.2 chapter was answered, more than 288 students have viewed the full step-by-step answer. The answer to “Refer to Example 4.14. Estimate the probability that exactly one of the four tires has a flaw, and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 24 words.

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Refer to Example 4.14. Estimate the probability that