Question

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 = 3.3. (Round your answers to two decimal places.)

(a) Compute a 95% CI for μ when n = 25 and x = 54.7.

(      ,        )   watts

(b) Compute a 95% CI for μ when n = 100 and x = 54.7.

(        ,     ) watts
(c) Compute a 99% CI for μ when n = 100 and x = 54.7

(          ,         ) watts
(d) Compute an 82% CI for μ when n = 100 and x = 54.7.

(          ,          ) watts
(e) How large must n be if the width of the 99% interval for μ is to be 1.0? (Round your answer up to the nearest whole number.)
n =

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

For normally distributed population with population standard deviation given, Confidence interval is given by,

Given,

a) 95% Confidence interval,

, n=25

Z-value for 95% confidence is 1.96

(53.41, 55.99)

b) 95% confidence interval,

, n=100

Z-value for 95% confidence is 1.96

( 54.05, 55.35)

c) 99% confidence interval,

, n=100

Z-value for 99% confidence is 2.58

( 53.85, 55.55)

d) 82% confidence interval,

, n=100

Z value for 82% confidence is 1.34

(54.26, 55.14)

e) 99% confidence, with  width =1

Total width=1, which means each tail would be 0.5

Z-value for 99% confidence is 2.58