Question

The average weight of 50 senior high school students is 52 kg with a standard deviation of 2.5

kg. If 25 students are randomly selected, find the mean, standard deviation, and variance of the

corresponding sampling distribution of the sample means

Answer 1

$E\bar{x}=\mu =52\\D\bar{x}=\frac{\sigma ^2}{\sqrt{n}}=\frac{2.5^2}{\sqrt{25}}=1.25\\\sigma \bar{x}=\sqrt{D\bar{x}}=\sqrt{1.25}=1.11803$