Question

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $165,000. This distribution follows the normal distribution with a standard deviation of $40,000. If we select a random sample of 50 households, what is the standard error of the mean

Answer 1

Answer: $5656.85

Step-by-step explanation:

The standard error of the mean measures the dispersion of sample means about the population mean .

It is also known as the standard deviation of its sampling distribution.

Formula : $SE=\dfrac{\sigma}{\sqrt{n}}$ , where $\sigma$ = population standard deviation.

n= sample size.

As per given , we have

$\sigma=\ 40,000$

sample size : n= 50

Then, the standard error of the mean will be :-

$SE=\dfrac{\ 40000}{\sqrt{50}}=\ 5656.85424949\approx\ 5656.85$

Hence, the standard error of the mean= $5656.85