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 40 cables and apply weights to each of them until they break. The 40 cables have a mean breaking weight of 775.3 lb. The standard deviation of the breaking weight for the sample is 14.9 lb.

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

Answer 1

Solution:

Given that

Number of samples n= 40

At 90% confidence interval

From normal distribution at 90% confidence interval

Margin of Error

                    

At 90% confidence interval the mean is

=

The 90% confidence interval is (771.44 ; 779.16)

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