Question

Suppose a simple random sample of size nequals41 is obtained from a population with muequals66 and sigmaequals16.​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample​ mean? Assuming the normal model can be​ used, describe the sampling distribution x overbar.

Answer 1

n = 41

`\mu = 66`

`\sigma = 16`

According to the central limit theorem

Let
`z=\frac{\bar{x}-\mu}{(\sigma)/(√(n))}` is a standard normal variable

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample​ mean?

Ans. The population must be normally distributed

b) Assuming the normal model can be​ used, describe the sampling distribution x over bar.

Approximately normal with
`\mu_{\bar{x}}=66`and
`\sigma_{\bar{x}}=(16)/(√(41))`