Question

Majesty Video Production Inc. wants the mean length of its advertisements to be 24 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 15 ads produced by Majesty. What can we say about the shape of the distribution of the sample mean time?

Answer 1

Answer:

It is going to be bell-shaped(normally distributed), with mean $\mu = 24$ and standard deviation $s = \frac{2}{\sqrt{15}} = 0.5164$.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$.

What can we say about the shape of the distribution of the sample mean time?

It is going to be bell-shaped(normally distributed), with mean $\mu = 24$ and standard deviation $s = \frac{2}{\sqrt{15}} = 0.5164$.