Question

5. A professional basketball team, has won 12 of its last 20 games and it is expected to continue winning at the same percentage rate. The team’s ticket manager is anxious to attract a large crowd (filling the team’s basketball arena) to next week’s game but believes that depends on how well the team performs tonight against its rival. Based on her past experience, she assese the probability of drawing a full-arena crowd to be 90 percent should the team win tonight. If we let X represent the number of wins for the team and L represent the number of losses for the team, the probabilities of X and L can be calculated using the binomial probability distribution. Please answer the following questions based on the information given in this problem.

b. What is the probability that the team loses less than half of its next 15 games? Show your work.   

c. What is the probability that the team wins at most 11 out of its next 15 games? Show your work.                                                            

d. What is the probability that the team loses more than 10 out of its next 15 games? Show your work.                                                                       

e. What is the probability that the team wins at least 6 out of its next 15 games? Show your work.

f. What is the probability that the team loses all of its next 15 games? Show your work.   

g. How many loses are expected for the team out of its next 15 games?

h. Calculate and interpret the standard deviation for the number of wins out of the next 15 games for the team. Show your work.

Answer 1

This is a case of binomial distribution with p = 12/20 = 0.6 (for wins) and p = 0.4 (for loss). Let A be the random variable then,

P(A=a) = (nCx)*px(1-p)n-x

B.

P(L7) = 0.7869

C.

P(X11) = 0.9095

D.

P(L>10) = 0.00935

E.

P(X6) = 0.9662

F.

P(L = 15) = 0.00000107374

G.

Expected losses = n*p

= 15*0.4

= 6

I.

Std. Deviation for the wins =

= 1.8974

That means when you play 15 games, and do that over and over, we can expect an std. deviation of about 1.8974 among the distribution of the wins.

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