In a metal fabrication process, metal rods are produced to a specified target length of 15 feet. Suppose that the lengths are normally distributed. A quality control specialist
Collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and
A standard deviation of 0.65 feet. The 95% confidence interval for the true mean length
Of rods produced by this process is
A) 14.544 to 15.056 ft.
B) 14.345 to 15.255 ft.
C) 13.912 to 15.688 ft.
D) 14.454 to 15.146 ft.
E) 13.834 to 15.766 ft.

Question

Quizplus · Accepted Answer

We can use the formula for the confidence interval for a population mean, which is:

CI = X̄ ± z*(σ/√n)

where X̄ is the sample mean, σ is the population standard deviation (unknown), n is the sample size, and z is the critical value for the desired confidence level. Since we want a 95% confidence interval, we can use the z-value for the 97.5th percentile, which is 1.96.

Plugging in the values from the problem, we get:

CI = 14.8 ± 1.96*(0.65/√16) = 14.8 ± 0.403

So the 95% confidence interval for the true mean length of rods produced by this process is (14.8 - 0.403) to (14.8 + 0.403), or 14.397 to 15.203 feet. The closest answer choice is D, 14.454 to 15.146 feet.

In a Metal Fabrication Process, Metal Rods Are Produced to a Specified