Suppose that every time Buster Posey comes to bat for the San Francisco Giants,

Question

Suppose that every time Buster Posey comes to bat for the San Francisco Giants, there is a 0.320 probability that he will get a hit (his batting average last season). In one particular game, Posey will bat 4 times. Let the random variable x represent the number of hits Posey will have in this game.

1. Does the variable x satisfy the requirements of a binomial distribution? If so, then which outcome is considered a "success" and which outcome is considered a "failure" on each trial?

2. Determine the values of n, p, and q for this binomial distribution.

3. Use the Binomial Probability Formula to complete the following probability model for X (write out the calculator functions you are using to calculate each probability)

X : 0 1 2 3 4

P(X):

Explanation / Answer

1) here as probability of getting a hit is independent from one bat to another therefore this follows binomial distribution.

here success is that  Posey will hit on a bat and failure is not hitting on a bat.

2) here n=4 ; p =0.320 and q =1-0.320 =0.680

3)

from binomial distribution function binompdf(n,p,x)

below is distribution of X:

x P(x) formula 0 0.2138 binompdf(4,0.32,0) 1 0.4025 binompdf(4,0.32,1) 2 0.2841 binompdf(4,0.32,2) 3 0.0891 binompdf(4,0.32,3) 4 0.0105 binompdf(4,0.32,4)

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