Question

A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 47 cables and apply weights to each of them until they break. The 47 cables have a mean breaking weight of 777.4 lb. The standard deviation of the breaking weight for the sample is 15.5 lb.

Find the 90% confidence interval to estimate the mean breaking weight for this type cable.

( , )

Your answer should be rounded to 2 decimal places.

Answer 1

Given,

n =47

X_bar = 777.4

s = 15.5

Now calculate 90% of confidence interval

CI = x_bar z*(s/n)  

z value for 90% confidence interval is 1.645.

CI = 777.4 1.645*(15.5/47)

= 777.4 3.719

CI = 777.4 - 3.719 and CI = 777.4 + 3.719

CI = 773.68 and CI = 781.12

Therefore 90% of confidence interval is (773.68,781.12).