Pepperoni Appreciation: Tony's Pizza Company finds that 60% of the general population likes pepperoni pizza. I buy pizza for 53 of my intro stats students and it turns out that only 23 of these students like pepperoni pizza.

(a) Assume the 60% value is accurate for all college students. In all random samples of 53 college students, what is the mean and standard deviation for the number of those who like pepperoni pizza? Round both answers to 1 decimal place. mean=

standard deviation=

(b) Convert the 23 out 53 students in my class to a z-score. Round your answer to 2 decimal places. z = (c) Using the normal approximation to the binomial distribution, what is the probability of getting 23 or fewer students who like pepperoni pizza in a randomly selected group of 53 students? Round your answer to 4 decimal places. P(x 23) = (d) Recognizing the probability in part (c) is below the benchmark value of 0.05, which of the statements could explain this unusually low appreciation for pepperoni? a) Perhaps the quoted value of 60% is not accurate.

b) Perhaps the quoted value of 60% does not apply to college students.

c)This unusual event may be due to random variation but it is not likely.

d) All of these statements provide a possible justification for what happened.