A high school baseball player has a 0.263 batting average. In one game, he gets 7 at bats. What is the probability he will get at least 3 hits in the game?

Question

A high school baseball player has a 0.263 batting average. In one game, he gets 7 at bats. What is the probability he will get at least 3 hits in the game?

Answer 1

The situation is a binomial situation:

1. categorical variable with only 2 categories - hit (success)or no hit (failure)
2. known probability of success - 0.263 batting average
3. fixed number of trials - 7 at bats
4. each at bat should be independent if the player has more than 70 "at bats."

The random variable is X = # hits in 7 at bats

The distribution of X is binomial with n = 7 and p = 0.263.

We want to find the probability that X is at least 3: P(X>=3)

You can solve with the formula found on your formula sheet for x = 3 + x = 4 + ... + x = 7. If you have a TI 83 or 84, you can use the function binomcdf:

P(X >=3) = 1 - P(X <= 2) = 1 - binomcdf(n=7, p=0.263, x=2) = 0.271