Derek Lee of the Chicago Cubs had the highest batting average inthe 2005 MLB sea

Question

Derek Lee of the Chicago Cubs had the highest batting average inthe 2005 MLB season.
His average was .355. So assume the probability of getting a hit is.355 for each time he
batted. In a particular game assume he batted three times. Let X =# of hits that Derrek
Lee got in that game.
Hint: the probability of getting a purple marble is .355, withreplacement, in 3 draws…
a. Determine the probability distribution for X.
b. Calculate the mean of X.
c. What is the probability of getting at least one hits?

Explanation / Answer

Product

0

  .4431     

.4878

            .1341             

x Probability (using binomial formulas)

Product

0 C(3,0)(.355)0(.645)3˜ .2683

0

1 C(3,1)(.355)1(.645)2˜ .4431

  .4431     

2 C(3,2)(.355)2(.645)1˜ .2439

.4878

3 C(3,3)(.355)3(.645)0˜ .0447

            .1341             

                      = 1 E[x]= 1.065  hits

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