Question

In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process: What is the standard deviation of the sampling distribution of the sample mean? A. 0.03 B. .01 C. .1732 D. .0577 E. .10

Answer 1

Answer:

E. .10

Step-by-step explanation:

The standard deviation of sampling distribution of sample mean=σxbar=?

σxbar=σ/√n where, σ is the population standard deviation and n is sample size

We are given the population variance σ²=0.03 and we can calculate the population standard deviation from it by taking square root of variance

σ=√σ²

σ=√0.03

σ=0.1732

The standard deviation of sampling distribution of sample mean=σxbar=σ/√n

We are selecting 3 bolts so, n=3

σxbar=0.1732/√3

σxbar=0.1732/1.732

σxbar=0.1

So, The standard deviation of sampling distribution of sample mean is 0.1.