Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 616 hours and a standard deviation of 54 hours. Random samples of 31 bulbs are drawn from this population, and the mean of each sample is determined. What is the standard error of the mean of the sampling distribution?

Answer 1

The standard error of the mean of the sampling distribution is

$$\sigma_{\bar{x}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{54}{\sqrt{31}}\approx9.70\ hours$$