Question

If an MLB batter has a 0.300 batting average. If that player has four at-bats in one game, what are the odds of him having 0 hits, any hits or all four? What is the expected value of hits made (np)? What is the standard deviation of hits made [√np(1-p)]? (show in excel with functions)

Answer 1

Let X denotes the number of successful hits out of 4 hits.

X ~ Binomial(n = 4, p = 0.3)

The probability mass function of X is

Now,

The probability having 0 hits

The probability having any hits

The probability having all four hits

The expected value of hits made = E(X) = 4*0.3 = 1.2

The standard deviation of hits made