Question

lifespans of televisions have a mean of 4.7 years and a standard deviation of 1.2 years. samples of 36 televisions are randomly selected. will the distribution of sample means be normally distributed?
yes, because ( ngeq30 ).
no, because ( ngeq30 ).
yes, because the original distribution was already normal.
no, since we dont know if lifespans of televisions are normally distributed.

Explanation:

Step1: Recall the Central Limit Theorem

The Central Limit Theorem states that for a sample of size \(n\), the sampling distribution of the sample mean \(\bar{X}\) is approximately normal if \(n\geq30\), regardless of the shape of the population distribution.

Step2: Check the sample size

Here, the sample size \(n = 36\) and \(36\geq30\).

Answer:

Yes, because \(n\geq30\).