Ohn Jay is a major league pitcher. He pitches like a robot, that is he pitches the same way to each batter. There is a. 56 probability that the first ball he pitches to a batter is a strike. (first-pitch strike). This is independent from batter to batter. Let X equal the number of first-pitch strikes John Jay throws in a game where he pitches to 15 batters. Let Y equal the number of batters he pitches to until he throws his 2nd first-pitch strike. (could be more than 15)

a. What is the probability X=13?

b. What is the standard deviation of X?

c. What is the probability that X > 10?

d. What is the probability that X ≥ 12?

e. What is the probability that Y = 3?

f. What is the probability that Y = 2?

Question

Mathematics

Ali Lutz

24 May, 04:28

Ohn Jay is a major league pitcher. He pitches like a robot, that is he pitches the same way to each batter. There is a. 56 probability that the first ball he pitches to a batter is a strike. (first-pitch strike). This is independent from batter to batter. Let X equal the number of first-pitch strikes John Jay throws in a game where he pitches to 15 batters. Let Y equal the number of batters he pitches to until he throws his 2nd first-pitch strike. (could be more than 15)

a. What is the probability X=13?

b. What is the standard deviation of X?

c. What is the probability that X > 10?

d. What is the probability that X ≥ 12?

e. What is the probability that Y = 3?

f. What is the probability that Y = 2?

+3

Answers (1)

Know the Answer?

Miley Dominguez · Answer 1

Step-by-step explanation:

Given;

Sample size, n = 15 probability of a first pitch strike, p = 0.56 Probability of not first pitch strike; q = 1 - p = 1 - 0.56 = 0.44 Applying binomial distribution; P (X = r) = nCr x P^r x (q) ^n-r

a) P (X = 13) = C (15,13) x 0.56^13 x (1-0.56) ^2 = 0.0108

b) Mean = np = 15 x 0.56 = 8.400

Standard deviation = √ (np (1-p)) = √ (15 x 0.56 x (1-0.56)) = 1.9225

c) P (X>10) = 1 - P (X≤10) = 1 - 0.8633 = 0.1367

d) P (X≥12) = P (X=12) + P (X=13) + P (X=14) + P (X=15) = 0.0498

e) P (Y=3) = C (3,1) x 0.56^1 x (1-0.56) ^2 x 0.56 = 0.1821

f) P (Y=2) = C (2,1) 0.56^1 x (1-0.56) ^1 x 0.56 = 0.2760