Question

a simple random sample of size ( n = 55 ) is obtained from a population with ( mu = 88 ) and ( sigma = 19 ). 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 must be normal. the underlying distribution only needs to be approximately normal.

Explanation:

According to the Central Limit Theorem, when the sample size \(n\) is large (\(n\geq30\)), the sampling distribution of the sample mean \(\bar{x}\) is approximately normal regardless of the shape of the underlying population distribution. Here, \(n = 55\geq30\). So the underlying distribution does not need to be exactly normal.

Answer:

The underlying distribution only needs to be approximately normal.