A certain baseball player hits a home run in 7% of his at-bats. Consider his at-bats as independent events. Find the probability that this baseball player hits more than 42 home runs in 800 at-bats?
A)0.93
B)0.9693
C)0.0307
D)0.07

Question

Quizplus · Accepted Answer

The probability of hitting a home run is 0.07. The probability of not hitting a home run is 1 - 0.07 = 0.93. The probability of hitting more than 42 home runs in 800 at-bats is the complement of the probability of hitting 42 or fewer home runs in 800 at-bats. The probability of hitting 42 or fewer home runs in 800 at-bats is the sum of the probabilities of hitting 0, 1, 2, ..., 42 home runs in 800 at-bats. This is a binomial distribution with n = 800 and p = 0.07. The probability of hitting more than 42 home runs in 800 at-bats is 1 - the sum of the probabilities of hitting 0, 1, 2, ..., 42 home runs in 800 at-bats. This can be calculated using a binomial distribution calculator or a statistical software package. The probability of hitting more than 42 home runs in 800 at-bats is approximately 0.9693.

A Certain Baseball Player Hits a Home Run in 7