Suppose that the New England Colonial baseball team is equally likely to win any

Question

Suppose that the New England Colonial baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of 30 Colonials games. a. Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. b. Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. (If necessary, consult a list of formulas.) a. b.

Explanation / Answer

Let X be a random variable denoting winning a baseball game.

then X~B(30,0.5)

p=0.5; since there is equally likely chances of winning and loosing

q=0.5

a) mean=E(x)=np=30*0.5=15

b)standard deviation = sd(x) = sqrt(var(x)) = sqrt(npq) =sqrt(30*0.5*0.5)= 2.7386

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