Question

The mean life expectancy of a certain type of light bulb is 895 hours with a standard deviation of 18 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 40?

Answer 1

Answer:

The approximate standard deviation of the sampling distribution of the mean for all samples with n = 40 is 2.8460.

Step-by-step 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 of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

What is the approximate standard deviation of the sampling distribution of the mean for all samples with n = 40?

We have that $\sigma = 18$

So

$s = \frac{18}{\sqrt{40}} = 2.8460$

The approximate standard deviation of the sampling distribution of the mean for all samples with n = 40 is 2.8460.