7.31 Exam performance An exam consists of 50 multiplechoice questions. Based on how much you studied, for any given question you think you have a probability of p = 0.70 of getting the correct answer. Consider the sampling distribution of the sample proportion of the 50 questions on which you get the correct answer.

a. Find the mean and standard deviation of the sampling distribution of this proportion.

b. What do you expect for the shape of the sampling distribution? Why?

c. If truly p = 0.70, would it be very surprising if you got correct answers on only 60% of the questions?

Justify your answer by using the normal distribution to approximate the probability of a sample proportion of 0.60 or less.