Answer to Question #265970 in Statistics and Probability for Lilliene

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.