A high school baseball player has a 0.221 batting average. In one game, he gets 7 at bats. What is the probability he will get at least 5 hits in the game?

Answer 1

Probability of at least 5 hits

= Probability of 7 hits + Probability of 6 hits + Probability of 5 hits

=(.227)^7 + 7(.779)(.227)^6 + 21(.779)^2(.227)^5

=.0000311 + .000958 + .0076811= .0086702= 0.87%

mean = .227(7) = 1.59 hits in 7 at bats

standard deviation for a binomial distribution = sqr(npq) = sqr(7(.227)(.779) = 1.113

(5-1.59)/1.113 = 3.41/1.113 = 3.06 z score which is less than 0.5%

with the empirical rule (100-99)/2 = .5, close to .87. the empirical rule is a close approximation. the normal distribution is a close approximation to the binomial distribution.