You measure the weights of a random sample of 400 male workers in the automotive industry. the sample mean is = 176.2 lbs. suppose that the weights of male workers in the automotive industry follow a normal distribution with unknown mean μ and standard deviation σ = 11.1 lbs. a 95% confidence interval for μ is:

A 95% confidence interval for μ is (175.287 lbs, 177.113 lbs).

Step-by-step explanation:

By the Central Limit Theorem, the mean of the sample is the same as the mean of the population. So:

Building the confidence interval:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which is the standard deviation of the population and n is the length of the sample. So

The lower end of the interval is the mean subtracted by M. So it is 176.2 - 0.9130 = 175.287 lbs

The upper end of the interval is the mean added to M. So it is 176.2 + 0.9130 = 177.113 lbs.

A 95% confidence interval for μ is (175.287 lbs, 177.113 lbs).

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step-by-step explanation: