Question

The age of individual students have normal distribution with mean 18.6 and standard deviation 1.24. At Buting Senior High School, there 76 students from HUMSS A and HUMSS B with the same distribution as the entire age of grade 11.

What is the sample variance?

Answer 1

Here, $\mu=18.6, \space \sigma=1.24, \space n=76$

Since the ages of 76 students from HUMSS A and HUMSS B has the same distribution as the entire age of grade 11 then, the sample standard deviation given by $\sigma_{\bar{x}}$ is,

$\sigma _{\bar{x}}=\sigma/\sqrt n=1.24/\sqrt{76}= 0.1422378$

The sample variance is given as,

$\sigma^2_{\bar{x}}=(\sigma_{\bar{x}})^2=0.1422378^2= 0.02023158$

Therefore, the sample variance is 0.02023158.