Question

a simple random sample of size ( n = 36 ) is obtained from a population with ( mu = 104 ) and ( sigma = 23 ).
pick the best statement from the options below that must be true regarding the sampling distribution of the sampling mean of ( x ) in order to use the normal model.
the underlying distribution only needs to be approximately normal.
the underlying distribution must be normal.

Explanation:

The Central Limit Theorem states that for a sample size \(n\geq30\), the sampling distribution of the sample mean \(\bar{x}\) is approximately normal, regardless of the shape of the population distribution. Here, \(n = 36\geq30\). So, the underlying distribution does not need to be normal (it just needs to have a finite mean \(\mu\) and finite standard deviation \(\sigma\)).

Answer:

The underlying distribution only needs to be approximately normal.