Assume that the number of curve balls a pitcher throws follows a Binomial model

ID: 3356041 • Letter: A

Question

Assume that the number of curve balls a pitcher throws follows a Binomial model and that there is a 30% chance that the pitcher throws a curve ball.

Let X denote the number of curve balls the pitcher throws out of 100 pitches.

1) Check that the conditions to use a Normal model to approximate the Binomial model are satisfied.

2) What is the mean for the Normal model?

3) What is the standard deviation for the Normal model?

4) Using this Normal model, find the probability that the pitcher throws at least 40 curve balls out of 100 pitches.

Let Y denote the number of home runs hit by a batter out of 70 pitches. On average, the batter hits home runs 5% of the time.

5) Check that the conditions to use a Poisson model to approximate the Binomial model are satisfied.

6) What is the mean for the Poisson model?

7) Using this Poisson model, find the probability that the batter hits at least 10 home runs.

PLEASE ANSWER ALL PARTS THANK YOU

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p = 0.3

a) n * p = 100 * 0.3 = 30 > 5

n(1 - p) = 100 * 0.7 = 70 > 5

So, assumption is satisfied to use normal model

b) Mean = n * p = 100 * 0.3 = 30

c) SD = sqrt(30 * 0.7)

SD = 4.58

d) P(X > 40)

z = (40 - 30)/4.58 = 2.18

P(z > 2.18) = 0.01463

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