Question

he lifespan of the Ebola virus on flat dry surfaces has a normal distribution with μ = 643.6 minutes and σ = 77.7 minutes. You monitor a random sample of size n = 61 . What is the mean of the distribution of sample means?

Answer 1

By the Central Limit theorem, the mean of the distribution of sample means is 643.6 minutes.

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 = (\sigma)/(√(n))`.

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

In this problem

The mean of the population is 643.6 minutes.

By the Central Limit theorem, the mean of the distribution of sample means is 643.6 minutes.