Question

The GPAs of entering freshmen at an elite university are known to be normally distributed with σ =.89. A random sample of 30 freshmen from the incoming class at a state university had a standard deviation of 1.7. What is the probability of getting a standard deviation of 1.7 or larger from a sample of size 3 if the distribution is normal with σ =.89?

Answer 1

( please revert if sample size is n=3 as in one place it is 30 and other it is 3 ; I am using 3 here)

as X² test statistic =(n-1)s²./$\sigma$²

P(s>1.7)=P(S² >2.89)=P((n-1)s²./$\sigma$² >(3-1)*2.89/0.89²)=P(X² >7.297) =0.0260

(Note: