Question

A simple random sample of size n=13 is obtained from a population with μ=67 and σ=16.

​(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample​ mean? Assuming that this condition is​ true, describe the sampling distribution of x.

​(b) Assuming the normal model can be​ used, determine ​P(x<70.9​).

​(c) Assuming the normal model can be​ used, determine ​P(x≥68.9​).

​(a) What must be true regarding the distribution of the​ population?

A. The population must be normally distributed.

B. The sampling distribution must be assumed to be normal.

C. The population must be normally distributed and the sample size must be large.

D. Since the sample size is large enough, the population distribution does not need to be normal.

​(b) ​ P(x<70.9​)=__ (Round to four decimal places as​ needed.)

​(c) P(x≥68.9​)=__ ​(Round to four decimal places as​ needed.)

Answer 1

​(a) What must be true regarding the distribution of the​population?

A. The population must be normally distributed.

(b) and (c)