Use excel. Tennis replay in the year that this xercise was written, there were 8

Question

Use excel. Tennis replay in the year that this xercise was written, there were 879 challenges made to referee calls in professional tennis singles play. Among those challenges, 231 challenges were upheld with the call overturned. Assume that in general, 25% of the challenges are successfully upheld with the call overturned.

A. If 25% rate is correct, find the probability that among the 879 challenges, the number of overturned is exactly 231.

B. If the 25% rate is correct, find the probability that among the 879 challenges, the number of overturned call is 231 or more. If the 25% rate is correct, is 231 overturned calls among 879 challenges a result that is significantly high?

Explanation / Answer

A) as we know that 25% of the challenges are successfully upheld we have

p=0.25 and we have n=879 challenges and we are planning to find the exact overturned probability for 231 and so we are looking for exactly successful challenges =x= 879-231 = 648

As we understand that we have to use binomial theorm for the same and so the equation is

P(X=x) = nCr * p^x *(1-p)^(n-x)

here we P(X=648)= 879C648 * 0.25^648 * 0.75^231 =to solve the same in excel use the following formula =

=COMBIN(879,648)*(0.25^648) *(0.75^231)

Which comes nearly to zero

B) now the questio changed from exactly 231 to 231 or more and so the x becomes 648 or less

so the answer will be

P(X=648)+P(X=647)+----P(X=0) which is nearly 1

and by solving the same we get the value as approximately 1 you can replicate the same formula shown above in excel 649 times (i.e. from x=0 to x=648) to get the answer

Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!

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