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 [tex]\mu[/tex] and standard deviation of the population [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
[tex]s = 0.5, n = 81[/tex]
So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = \frac{\sigma}{\sqrt{81}}[/tex]
[tex]\sigma = 9*0.5 = 4.5[/tex]
The standard deviation of the population is 4.5 minutes.
