A high school baseball player has a 0.174 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 4 hits in the game?

Question

A high school baseball player has a 0.174 batting average. In one game, he gets 9 at bats. What is the probability he will get at least 4 hits in the game?

Answer 1

use a binomial distribution, as there are 2 disjoint mutually exclusive events, either a hit or no hit

n = 9, p = .174, q= .826

mean = np = 9(.174) = 1.566 expected hits for 9 times at bat

variance = npq = 9(.174)(.826)

sd = sqrVar = 3sqr(.174(.826) = about 1.1373

use z tables or t tables to find the area under a bell shaved curve to the right of the

z score for hits = 4

z = (4-1.566)/1.1373 = 2,434/1.1373 = about 2.1402

by the empirical rule odds of getting 4 or more hits is less than 2.5%

P(4 or more) = 1.617% using z tables or a z calculator