A softball pitcher has a 0.507 probability of throwing a strike for each pitch. If the softball pitcher throws 15 pitches, what is the probability that more than 8 of them are strikes? (Round your answer to 3 decimal places if necessary.)

P(X > 8) = 0.323

Step-by-step explanation:

We are given that a softball pitcher has a 0.507 probability of throwing a strike for each pitch. Also, the softball pitcher throws 15 pitches.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 15 pitches

            r = number of success = more than 8

           p = probability of success which in our question is probability of    

                 throwing a strike for each pitch, i.e., 0.507

LET X = Number of strikes

So, it means X ~

So, Probability that more than 8 of them are strikes = P(X > 8)

P(X > 8) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= =

= 0.323

Therefore, probability that more than 8 of them are strikes is 0.323.