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?

0.4801

Step-by-step explanation:

This is a binomial distribution question.

It can be approximated using normal distribution if the following conditions are met:

np > 10

n(1-p) > 10

Here,

n = 29

p = 0.487

So,

np = 14.12

n(1-p) = 14.88

So, we can use normal approximation here:

Binomial:  X ~ B(n,p)  becomes

Normal Approx:  X~ N()

Mean is:

Standard Deviation is:

We need probability of less than or equal to 14, so we can say:

P(x ≤ 14)

Using  , we have:

P(x ≤ 14) =

Note: We used z table in the last line

So the probability is 0.4801

answer: your correct answer is b. d.

step-by-step explanation: