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# In a sample of 60 electric motors, the average efficiency ISBN: 9780073401331 38

## Solution for problem 10E Chapter 5.1

Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

Problem 10E

In a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2.

a. Find a 95% confidence interval for the mean efficiency.

b. Find a 99.5% confidence interval for the mean efficiency.

c. What is the confidence level of the interval (84.63, 85.37)?

d. How many thermostats must be sampled so that a 95% confidence interval specifies the mean to within ±0.35?

e. How many thermostats must be sampled so that a 99.5% confidence interval specifies the mean to within ±0.35?

Step-by-Step Solution:
Step 1 of 3

Solution 10E

Step1 of 6:

Let us consider a random variable X it represents the efficiency of electric motors. Here random variable X follows normal distribution with mean standard deviation and n = 60.

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% confidence interval for the mean efficiency.

b). We need to find a 99.5% confidence interval for the mean efficiency.

c). We need to find the confidence level of the interval (84.63, 85.37).

d). We need to find a 95% confidence interval specifies the mean to within e). We need to find a 99.5% confidence interval specifies the mean to within Step2 of 6:

a).

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

Now,  = 0.025

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 0.9750 value falls, it falls in row 1.9 under column 0.06.

Hence, 95% confidence interval for the mean efficiency is given by    (84.4939, 85.5060)

Hence, 95% confidence interval for the mean efficiency is (84.4939, 85.5060).

Step3 of 6:

b).

Here we have to find 99.5%  CI, let us take .

Now,  = 0.0025

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 0.9975 value falls, it falls in row 2.8 under column 0.00.

Hence, 99.5%...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

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 “In a sample of 60 electric motors, the average efficiency (in percent) was 85 and the standard deviation was 2.a. Find a 95% confidence interval for the mean efficiency.________________b. Find a 99.5% confidence interval for the mean efficiency.________________c. What is the confidence level of the interval (84.63, 85.37)?________________d. How many thermostats must be sampled so that a 95% confidence interval specifies the mean to within ±0.35?________________e. How many thermostats must be sampled so that a 99.5% confidence interval specifies the mean to within ±0.35?” is broken down into a number of easy to follow steps, and 84 words. Since the solution to 10E from 5.1 chapter was answered, more than 714 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 10E from chapter: 5.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: interval, confidence, mean, efficiency, specifies. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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In a sample of 60 electric motors, the average efficiency

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