1.6.58 Multiple-choice questions on Advanced Placement exams have five options: A, B, C, D, and E. Arandom sample of the correct choice on 400 multiple-choice questions on a variety of AP exams shows thatB was the most common correct choice, with 90 of the 400 questions having B as the answer. Does thisprovide evidence that B is more likely than 20% to be the correct choice?

a.State hypotheses, and calculate the sample statistic.

b.Are conditions met for using a Normal distribution for this test? Explain.

c.Calculate the standard error and z-test statistic, assuming a Normal distribution is appropriate.

d.Find the p-value and draw a Normal curve with appropriate shaded region.p-value:

e.State the conclusion of the test in context, using nontechnical language.

f.Find a 95% confidence interval for the proportion of questions on all AP exams having B as the correct choice using the normal distribution and the formula for standard error. Show your calculations