Question

In 2014, there were 765 changes made to referee calls in professional singles tennis play. Among those challenges, 318 were upheld with the call overturned. Assume that 35% of the challenges are successfully upheld with the call overturned. Note: Round all probability answers to four (4) decimal places.

1. Of the 765 challenges, the number of 318 overturned calls is greater than 35%. Using the normal approximation to the binomial, find the probability that among the 765 challenges, the number of overturned calls is 318 or fewer. If the 35% rate is correct, is 318 overturned calls for 765 challenges unusually low?

Answer 1

Here we have

n=765 and p=0.35

Since np = 267.75 and n(1-p) = 497.25 both are greater than 5 so we can use normal approximation here.

Using normal approximation, X has approximately normal distribution with mean and SD as follows:

The z-score for X = 318 +0.5 = 318.5 is

The probability that among the 765 challenges, the number of overturned calls is 318 or fewer is

No it is not unusual.