Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size of 6, answer these questions:

Part A: What is the standard deviation of the sampling distribution of x? Show your

work. (5 points)

Part B: What does the sample size need to be if you want the standard deviation of

the sampling distribution of x to be 0.325? Show your work.

A) standard deviation of the sampling distribution of x is 0.5307

B) the sample size needs to be 16, if you want the standard deviation of   the sampling distribution of x to be 0.325

Step-by-step explanation:

Given that;

Population mean μ = 53.7

standard deviation σ = 1.3

sample size n = 6

Sampling distribution of x" follows Normal distribution

x" η N ( μ_x" =μ, σ_x"= σ/√n)

A)

standard deviation of the sampling distribution of x

⇒X" = σ_x" = σ/√n

we substitute

= 1.3/√6

= 1.3 / 2.4494

= 0.5307

Therefore standard deviation of the sampling distribution of x is 0.5307

B)

if σ_x" = 0.325

⇒  σ/√n = 0.325

we substitute in the value of σ

⇒ 1.3/√n = 0.325

√n = 1.3 / 0.325

√n = 4

n = 4²

n = 16

Therefore the sample size needs to be 16, if you want the standard deviation of   the sampling distribution of x to be 0.325