Question

A simple random sample of size n=11 is obtained from a population with μ=68 and σ=17.

​(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 barx.

​(b) Assuming the normal model can be​ used, determine ​P(bar x < 71.4​).

​(c) Assuming the normal model can be​ used, determine ​P(bar x ≥ 69.6​).

Answer 1

The distribution of population must be normal and using central limiting theorem the distribution of is normal with mean and standard deviation

We define the standard random variable Z as

b) Using Normal table we have

c)