Answer to Question #296057 in Statistics and Probability for secret

Question

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equal to 777 hours and a standard deviation of 26 hours. Random samples of 30 bulbs are drawn from this population, and the mean of each sample is determined. What is the mean of the mean of the sampling distribution?

Answer 1

According to the central limit theorem, distribution of the sample mean is

X~$N(x, {\frac {\sigma} {\sqrt n}})$ , where X - sample mean, x - distribution mean, $\sigma$ - distribution standard deviation. So, the mean of the mean would be the mean of the considered random variable. In our case it is 777 hours