Question

A quality control engineer Is interested in the mean length of sheet insulation being cut automatically by machine. It is known that the standard deviation in the cutting length that this machine produces is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a confidence interval for the mean length cut by machine. Referring to problem statement, the Z value to use in obtaining the 99% confidence interval is approximately .A.1.645B. 1.96C.3.23D.2.58

Answer 1

D.2.58

Explanation:

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

`\alpha = (1 - 0.99)/(2) = 0.005`

Now, we have to find z in the Ztable as such z has a pvalue of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.005 = 0.995`, so Z = 2.58.

The answer is given by option D.