Question 523347: A basketball team's star 3-point shooter takes six 3- point shots in a game. Historically, he makes 40% of all 3-point shots taken in a game. State at the outset what assumptions you have made.
(a) Find the probability that at least two shots were made.
(b) Find the probability that exactly three shots were made.
(c) Find the mean and standard deviation of the num¬ber of shots made.
(d) Find the mean and standard deviation of the total number of points scored as a result of these shots.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A basketball team's star 3-point shooter takes six 3- point shots in a game. Historically, he makes 40% of all 3-point shots taken in a game. State at the outset what assumptions you have made.
Independent trials; binomial results;
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(a) Find the probability that at least two shots were made.
P(2<= x <= 6) = 1 - binomcdf(6,0.4,1) = 0.7667
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(b) Find the probability that exactly three shots were made.
P(x = 3) = 6C3*0.4^3*0.6^3 = 0.2765
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(c) Find the mean and standard deviation of the num¬ber of shots made.
mean = np = 6*0.4 = 2.4
std = sqrt(npq) = sqrt(2.4*0.6) = 1.2
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(d) Find the mean and standard deviation of the total number of points scored as a result of these shots.
mean # of points: 2.4*3 = 7.2
std of # of points: 1.2*3 = 3.6
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Cheers,
Stan H.
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