QUESTION 3 (BINOMIAL MODEL) Assume that the number of curve balls a pitcher thro

Question

QUESTION 3 (BINOMIAL MODEL)

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.

1) What is the expected number of curve balls the pitcher throws out of 10 pitches?

2) What is the standard deviation for the number of curve balls the pitcher throws out of 10 pitches?

3) What is the probability that the pitcher throws exactly 2 curve balls out of 10 pitches?

4) What is the probability that a pitcher throws no curve balls out of 15 pitches?

5) What is the probability that the pitcher throws at least 2 curve balls out of 15 pitches?

6) What is the probability that a pitcher throws at least 13 curve balls out of 15 pitches?

PLEASE ANSWER ALL PARTS THANK YOU

Explanation / Answer

Let the number of curve balls a pitcher throws be X

So, X follows Binomial with p = 0.3

(a) E(X) = np where n = 10

So, E(X) = 10*0.3 = 3

(b) standard deviation = (np(1-p))0.5

Standard dev = (10*0.3*07)0.5 = 1.4491

(c) P(X=2) = 10C2 (0.3)2 (0.7)10-2 = 0.2335

(d) P(X=0) = n is now 15 , required probability = 15C0(0.3)0 (0.7)15-0 = 0.0047

(e) P(X>=2) = 1-P(X<2)

=1-(P(X=0)+P(X=1))

=1-(0.0047+15C1(0.3)1 (0.7)15-1 ) = 0.9648

(f) P(X>=13) = P(X=13)+P(X=14)+P(X=15)

= 15C13(0.3)13 (0.7)15-13 +15C14(0.3)14 (0.7)15-14 +15C15(0.3)15 (0.7)15-15

=0.0000087

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