Achievement test scores of all high school seniors in a Canadian province have mean 60 and standard deviation 8. A random sample of n = 100 students from one large high school in this province had a mean score of 58.

(a) Describe the approximate distribution of the sample mean achievement test scores of high school seniors.

(b) Describe how the distribution of the sample mean achievement test scores would change if a larger sample of students were taken.

(c) Is there any evidence to suggest that this high school is inferior? Test at a significance level of = 0.05.