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?

Answer 1

0.4801

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(
`np,√(np(1-p))`)

Mean is:

`\mu=np=14.123`

Standard Deviation is:

`\sigma=√(np(1-p)) =2.69`

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

P(x ≤ 14)

Using
`z=(x-\mu)/(\sigma)`, we have:

P(x ≤ 14) =
`P((x-\mu)/(\sigma) \leq (14-14.123)/(2.69))\\=P(z \leq -0.05)\\=0.4801`

Note: We used z table in the last line

So the probability is 0.4801