Quiz 3

M 154a, Oct. 24, 1997
      Name:       ID:

In baseball, a batting average is the probability that a batter will hit the ball while at bat. A certain player has a batting average of 0.400 (for some reason, batting averages are always given to three decimal places.) We are interested in calculating the probability that the batter hits at least 1 ball (that is, 1 or more), in his next ten at-bats (attempts.)

1.

(3) It seems reasonable to apply the binomial probability model here. Why? List the assumptions of the model and explain why they apply. Solution: There are a fixed number of trials (10). We must assume the outcome of each trial is independent. And the probability of a hit remains the same from trial to trial. (In real life these assumptions should be checked carefully, since they might not be true.) And obviously, the outcome of each trial is either success (a hit) or failure (a miss).

2.

(7) What is the probability that the batter hits at least 1 ball in his next ten at-bats? You do not need a probability table, but will need a calculator.

Solution Let X be the number of hits in ten at-bats. Then we want ${\mbox P}(X \ge 1) = 1 - {\mbox P}(X = 0) =1- .6^{10} = .9940$