Suppose there were 661 challenges made to referee calls in t

Suppose there were 661 challenges made to referee calls in tennis singles play. Assuming that 30% of challenges are successfully upheld with the referee call being overturned, find the probability that the number of overturned calls is fewer than 172

Solution

mean=n*p= 661*0.3 =198.3

standard deviation =sqrt(n*p*(1-p)) = sqrt(661*0.3*0.7) =11.78177

So the probability that the number of overturned calls is fewer than 172 is

P(X<172) = P((X-mean)/s <(172-198.3)/11.78177)

=P(Z<-2.23) = 0.0129 (from standard normal table)