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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.1 - Problem 16e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.1 - Problem 16e

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# Refer to Exercise 9.a. Find a 90% upper confidence bound

ISBN: 9780073401331 38

## Solution for problem 16E Chapter 5.1

Statistics for Engineers and Scientists | 4th Edition

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Problem 16E

Problem 16E

Refer to Exercise 9.

a. Find a 90% upper confidence bound for the mean weight.

b. Someone says that the mean weight is less than 1.585 g. With what level of confidence can this statement be made?

Step-by-Step Solution:
Step 1 of 3

Solution 16E

Step1 of 3:

Let us consider a random variable X it represents the weight of the penny nail. Here random variable X follows normal distribution with mean standard deviation and

n = 80.

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 90% upper confidence bound for the mean weight.

b). We need to find level of confidence can this statement be made by taking the mean weight is less than 1.585 g.

Step2 of 3:

a).

Here we have to find 90%  CI, let us take .

Now,

= 0.10

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 0.90 value falls, it falls in row 1.2 under column 0.08.

Hence,

90% upper confidence bound for the mean weight is given by

(1.5743)

Hence, 90% upper confidence bound for the mean weight is 1.5743.

Step3 of 3:

b).

We have and n = 80.

In a given information we have upper bound 1.585

Now,

1.585 - 1.56 = (0.0111)

0.025 =  (0.0111)

=

= 2.2522

Hence, = 2.25.

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 2.2 under column 0.05.

= 0.9878

Area to the right of Z is  1 - 0.9878

= 0.0122

Hence level is 0.0122.

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

This full solution covers the following key subjects: weight, confidence, mean, made, less. 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. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 16E from chapter: 5.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Since the solution to 16E from 5.1 chapter was answered, more than 458 students have viewed the full step-by-step answer. The answer to “Refer to Exercise 9.a. Find a 90% upper confidence bound for the mean weight.________________b. Someone says that the mean weight is less than 1.585 g. With what level of confidence can this statement be made?” is broken down into a number of easy to follow steps, and 35 words.

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