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Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809

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BuyFindarrow_forward

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
ISBN: 9781305251809
Textbook Problem

A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with σ = 3.0.

  1. a. Compute a 95% CI for μ when n = 25 and x ¯ = 58.3.
  2. b. Compute a 95% CI for μ when n = 100 and x ¯ = 58.3.
  3. c. Compute a 99% CI for μ when n = 100 and x ¯ = 58.3.
  4. d. Compute an 82% CI for μ when n = 100 and x ¯ = 58.3.
  5. e. How large must n be if the width of the 99% interval for μ is to be 1.0?

a.

To determine

Find the 95% confidence interval for population mean stray load loss.

Explanation

Given info:

n=25, x¯=58.3,σ=3.0 and 95% confidence level.

Calculation:

Confidence interval:

Software Procedure:

Step by step procedure to obtain the 95% confidence interval to estimate the population mean stray load loss using the MINITAB software:

  • Choose Stat > Basic Statistics > 1-Sample z.
  • In Summarized data, enter the sample size as 25, sample mean as 58.3.
  • Enter population standard deviation as 3.0.
  • In Options, enter Confidence level as 95

b.

To determine

Find the 95% confidence interval for population mean stray load loss.

c.

To determine

Find the 99% confidence interval for population mean stray load loss.

d.

To determine

Find the 82% confidence interval for population mean stray load loss.

e.

To determine

Find the number of induction motors required to be sampled for the width of the 99% confidence interval to be 1.0.

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