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Benny

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Q. Two tennis professionals, A and B, are scheduled to play a 'best of five sets' match, for which the winner is the first player to win three sets in a total that cannot exceed five sets. The probability that A wins anyone set is 0.6, independent of the outcome of any other set. Let X denote the number of sets played in the match. Then the distribution of X is given by:

Code:

```
x | 3 4 5
-----------------------------------
Pr(X=x) | 0.280 0.374 0.346
```

(a) Show that the mean and standard deviation of X are 4.066 and 0.788 (correct to three decimal places), respectively.

(b) Over a year, the two players play each other in 16, best of five sets, matches. Find the mean and standard deviation of T, the total number of sets they play in the 16 matches and, using a normal approximation with continuity correction, find Pr(T>=70).

The first one is just plugging values into formulas but I don't know how to start the second part. I think it has something to do with the binomial distribution. There is a fixed number of matches (16) but I don't know how to relate the information in part (a) to part (b).

Can someone help me out? Thanks.