Answer:
The mean of of the sample mean of these quality checks is 10 and the standard deviation is 0.7155.
Step-by-step explanation:
To solve this question, we use the central limit theorem.
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 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 = 10, \sigma = 1.6, n = 5, s = \frac{1.6}{\sqrt{5}} = 0.7155[/tex]
The mean of of the sample mean of these quality checks is 10 and the standard deviation is 0.7155.