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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?

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4 votes

Answer:

It is going to be bell-shaped(normally distributed), with mean
\mu = 24 and standard deviation
s = (2)/(√(15)) = 0.5164.

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
(\sigma)/(√(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 = (2)/(√(15)) = 0.5164.

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