A baseball player, Mickey, who bats 310 (or .310) gets an
average of 3.1 hits in ten at bats. We will assume that each time
Mickey bats he has a 0.31 probability of getting a hit. This means
Mickeys at bats are independent from one another. If we also assume
Mickey bats 5 times during a game and that x= the number of hits
that Mickey gets then the following probability mass function,
p(x), and cumulative distribution function F(x) are
reasonable:
x | 0 | 1 | 2 | 3 | 4 | 5 |
p(x) | .156 | .351 | .316 | a | .032 | .003 |
F(x) | .156 | .507 | .823 | b | .997 | 1.00 |
g. Assume Mickey bats exactly 5 times (a 5-at-bat-game) in each of four consecutive games. What is the probability he gets 2 hits in exactly 2 of those 4 games? (Getting exactly 2 hits will be called a 2-hit-game.)
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