Question

A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard deviation 3.5 psi. How is the standard deviation of the sample mean changed when the sample size is increased from n equals 9 to n equals 45 ? Round all intermediate calculations to four decimal places (e.g. 12.3456) and round the final answer to three decimal places (e.g. 98.768). The standard deviation is by psi.

Answer 1

When the sample size is increased from n = 9 to n = 45, the standard deviation of the sample mean decreases from 1.167 to 0.522.

Explanation:

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 = (\sigma)/(√(n))`

In this problem, we have that:

`\sigma = 3.5`

n = 9

`s = (3.5)/(√(9)) = 1.167`

n = 45

`s = (3.5)/(√(45)) = 0.522`

When the sample size is increased from n = 9 to n = 45, the standard deviation of the sample mean decreases from 1.167 to 0.522.