Question

A softball pitcher has a 0.487 probability of throwing a strike for each pitch. If the softball pitcher throws 29 pitches, what is the probability that no more than 14 of them are strikes? Insert the correct symbol to represent this probability.

Answer 1

P(x≤14) = 0.556

Explanation:

Given:

Probability of throwing a strike (p) = 0.487

Total number of throw (n) = 29

Find:

Probability that no more than 14 of them are strikes P(x≤14)

Computation:

Mean(np) = (29)(0.487)

Mean(np) = 14.123

Standard deviation = √[mean( 1- p)]

Standard deviation = √[14.123( 1 - 0.487)]

Standard deviation = 2.6917 (Approx)

P(X < x) = P[(Z < (x - mean)]/[Standard deviation])

P(x≤14) = P(Z < (14.5 - 14.123) / 2.6917 )

P(x≤14) = 0.556