Question

A nail fabrication machine makes nails with a target length of μ = 2.35 inches. The machine has some variability, so the standard deviation of the length is σ = 0.2 inch. The machine operator inspects a random sample of 10 nails each hour for quality control purposes and records the sample mean diameter, x. Assuming the process is working properly, what are the mean and standard deviation of the sampling distribution of x?

μx= 2.35 and σx= 0.2
μx= 10 and σx= 0.0632
μx= 10 and σx= 0.2
μx= 2.35 and σx= 0.0632
μx = 2.35 and σx= 3.16

Answer 1

μx= 2.35 and σx= 0.0632

Explanation:

The machine is working properly, so the sample mean μx equals the population mean μ = 2.35.

The sample standard deviation is:

σx = σ / √n

σx = 0.2 / √10

σx = 0.0632