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

Answer:

The standard deviation of the population is 4.5 minutes.

Step-by-step 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 $s = \frac{\sigma}{\sqrt{n}}$.

In this question:

$s = 0.5, n = 81$

So

$s = \frac{\sigma}{\sqrt{n}}$

$0.5 = \frac{\sigma}{\sqrt{81}}$

$\sigma = 9*0.5 = 4.5$

The standard deviation of the population is 4.5 minutes.