SOLUTION: Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of Colonials games.

Algebra ->  Probability-and-statistics -> SOLUTION: Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of Colonials games.      Log On


   

Question 1183733: Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of Colonials games.
Answer the following.
(If necessary, consult a list of formulas.)
(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.
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.

Suppose the random sample consists of n games.


The probability distribution to have k games win is the binomial distribution with the number of trials n,
the number of successful trials k and the probability of success of 1/2 for each single game


    P(n,k,p) = P(n,k,0.5) = C%5Bn%5D%5Ek%2A0.5%5Ek%2A0.5%5E%28n-k%29 = %28n%21%2F%28k%21%2A%28n-k%29%21%29%29%2A0.5%5En.


Estimation of the number of games in the sample that the Colonials win is the mean of this distribution  


                          p*n = 0.5*n.    ANSWER