Question

The average weight of 52 senior high school students is 50 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 sample means.

Answer 1

$\mu_{\bar X}=\mu=50.$

$\sigma_{\bar X}=\frac{\sigma}{\sqrt{n}}\sqrt{\frac{N-n}{N-1}}=\frac{2.5}{\sqrt{25}}\sqrt{\frac{52-25}{52-1}}=0.3638.$

$\sigma^2_{\bar X}=0.3638^2=0.1324.$