Question

Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0.5 minutes. What is the standard deviation of the population?

Answer 1

The standard deviation of the population is 4.5 minutes.

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation of the population
`\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))`.

In this question:

`s = 0.5, n = 81`

So

`s = (\sigma)/(√(n))`

`0.5 = (\sigma)/(√(81))`

`\sigma = 9*0.5 = 4.5`

The standard deviation of the population is 4.5 minutes.