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

$\mu_X=\mu=50$

$\sigma_X=\frac{\sigma}{\sqrt{n}}\sqrt{\frac{N-n}{N-1}}=\frac{2.5}{\sqrt{25}}\sqrt{\frac{52-25}{52-1}}=0.3638$

$\sigma^2_X=0.3638^2=0.1324$