Question

Wasserman (1989) studied a process for the manufacturing of steel bolts. Historically, these bolts have a mean thickness of 10.0 mm and a standard deviation of 1.6 mm. In a quality check, the engineer has a sample of 5 randomly selected and measured.
Assuming a near-normal distribution, what are the mean and standard deviation of the sample mean of these quality checks?

Answer 1

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 $\mu$ and standard deviation $\sigma$, 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 problem, we have that:

$\mu = 10, \sigma = 1.6, n = 5, s = \frac{1.6}{\sqrt{5}} = 0.7155$

The mean of of the sample mean of these quality checks is 10 and the standard deviation is 0.7155.