Question

A baseball player has a lifetime batting average of 0.228. If, in a season, this player has 380 "at bats", what is the probability he gets 78 or more hits?

Probability of 78 or more hits =

Answer 1

Solution :

Given that,

Using binomial distribution,

= n * p = 0.228 * 380 = 86.64

= n * p * q = 380 * 0.228 * 0.772 = 8.1784

Using continuity correction ,

P(x 77.5) = 1 - P(x   77.5)

   = 1 -  P[(x - ) / (77.5 - 86.64) / 8.1784]

= 1 -  P(z -1.12)  

= 0.8686

Probability of 78 or more hits = 0.8686