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Refer to Exercise 7.a. Find a 95% lower confidence bound

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

Solution for problem 14E Chapter 5.1

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 14E

Problem 14E

Refer to Exercise 7.

a. Find a 95% lower confidence bound for the mean capacity of this type of battery.

b.An engineer claims that the mean capacity is greater than 175 ampere-hours. With what level of confidence can this statement be made?

Step-by-Step Solution:
Step 1 of 3

Solution 14E

Step1 of 3:

Let us consider a random variable X it represents the capacity of batteries. Here random variable X follows normal distribution with mean standard deviation and n = 120.

That is

                       

The probability density function of normal distribution is given by

, .

Where,

x = random variable

= mean of X

= variance of X

= standard deviation os X

= mathematical constant and its value is 3.14

Here our goal is:

a). We need to find a 95% lower confidence bound for the mean capacity of this type of battery.

b). We need to find level of confidence can this statement be made, by taking the mean capacity is greater than 175 ampere-hours.


Step2 of 3:

a).

Here we have to find 95%  CI, let us take .

Now,

 

   = 0.05

Z-scores(are to the right) is given by

                                                                       

is obtained from standard normal table(area under normal curve). In standard normal table we have to see where 0.95 value falls, it falls in row 1.6 under column 0.04.

Hence,

95% lower confidence bound for the mean capacity of this type of battery is given by

   

     

         

                                                (175.9040)

Hence, 95% lower confidence bound for the mean capacity of this type of battery is 175.9040.


Step3 of 3:

b).

We have and n = 120.

In a given information we have lower bound 175

Now,

                 

                         

          175 - 178 = (1.2780)

                       -3 =  (1.2780)

                                                       =

         = -2.3474

Hence, = -2.34.

Z-scores is given by , and this value is obtained from standard normal table(area under normal curve). In standard normal table we have to see in row -2.3 under column 0.04.

 = 0.0096

Area to the right of Z is  1 - 0.0096

                                     = 0.9904.

Hence level is 0.9904.


Step 2 of 3

Chapter 5.1, Problem 14E is Solved
Step 3 of 3

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

The full step-by-step solution to problem: 14E from chapter: 5.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 14E from 5.1 chapter was answered, more than 453 students have viewed the full step-by-step answer. This full solution covers the following key subjects: capacity, mean, confidence, Find, claims. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “Refer to Exercise 7.a. Find a 95% lower confidence bound for the mean capacity of this type of battery.________________b.An engineer claims that the mean capacity is greater than 175 ampere-hours. With what level of confidence can this statement be made?” is broken down into a number of easy to follow steps, and 40 words.

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Refer to Exercise 7.a. Find a 95% lower confidence bound