Before creating the final exam this semester, your psychology teacher decided to estimate the average test score of the final exams from past years. The teacher has gathered a random sample of 120 student exams from previous years. They have found that there is an average score of 85% with a standard deviation of 11%.

a) Construct a 90% confidence interval for the true average test score of psychology students.

b) Interpret your results from part a in the context of this problem.

c)Suppose the teacher wanted to make a 99% confidence interval instead. What would happen to the width of the interval?(You do NOT need to calculate the interval)

d)the teacher also observed that out of the 120 sampled exams, 96 of them were passing grades. Construct a 95% confidence interval for the true proportion of students that pass the exam.

e)Interpret the interval in part d in the context of this problem.