In the year that this exercise was written, there were 611 challenges made to referee calls in professional tennis singles play. Among those challenges, 172 were upheld with the call overturned. Assume that 30% of the challenges are successfully upheld with the call overturned.
a. Find the probability that among the 611 challenges, the number of overturned calls is exactly 172.
b. Of the 611 challenges, the number of 172 overturned calls is fewer than 30%. Find the probability that among the 611 challenges, the number of overturned calls is 172 or fewer. If the 30% rate is correct, is 172 overturned calls for 611 challenges an unusually low number?
c. Which result is useful for determining whether the 30% rate is correct: part (a) or part (b)? Explain.
d. Is there strong evidence to suggest that the rate of overturned calls is not 30%?