Question

A team of employees at a company has daily meetings that are scheduled to take 30 minutes, and sometimes they go for the full time, but they often only last a few minutes. The mean duration of these meetings is 20 minutes and the standard deviation is 10 minutes. Suppose that we take random samples of 5 meetings from this population and calculate X bar as the sample mean duration. What will be the shape of the distribution of (X bar) ?(Select one)
a.Skewed to the left

b.Skewed to the right

c.Approximately normal

d.Unknown, we don’t have enough information to determine the shape

Answer 1

Answer:

d.Unknown, we don’t have enough information to determine the shape

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

We don't know the shape of the distribution of the meetings time.

The sample size is smaller than 30.

So we can't apply the central limit theorem, and the correct answer is:

d.Unknown, we don’t have enough information to determine the shape