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 0.20 feet. A sample of 75 cut sheets yields a mean length of 12.25 feet. This sample will be used to obtain a confidence interval for the mean length cut by machine. Referring to Scenario 1, the Z value to use in obtaining the 95% confidence interval is approximately .

A. 2.58.
B.1.96.
C. 1.75.
D. 1.645.

Answer 1

Answer: B.1.96.

Explanation:

The critical z-value used for
`(1-\alpha)` confidence interval istwo tailed value with the significance level of
`(\alpha)` i.e.
`z_(\alpha/2)` from the standard normal distribution table for z.

Given : Level of confidence :
`1-\alpha=0.95`

Significance level :
`\alpha:1-0.95=0.05`

By using the standard normal distribution table for z,

The z-value =
`z_(0.05/2)=z_(0.025)=1.96`