Answer:
Mean 105
Standard deviation 1.89
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 105, \sigma = 17[/tex]
If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.
By the Central limit theorem
mean 105
Standard deviation
[tex]s = \frac{17}{\sqrt{81}} = 1.89[/tex]
