There is a 0.1019 probability that a best-of-seven contest will last four games,

Question

There is a 0.1019 probability that a best-of-seven contest will last four games, a 0.1853 probability that it will last five games, a 0.1897 probability that it will last six games, and a 0.5231 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation. Is it unusual for a team to "sweep" by winning in four games? What is the mean of the probability distribution? What is the standard deviation of the probability distribution? Is it unusual for a team to win in four games? Choose the correct answer below. Yes, because the probability that a team wins in four games is greater than 0.05. No. because the probability that a team wins in four games is less than or equal to 0.05. Yes, because the probability that a team wins in four games is less than or equal to

Explanation / Answer

Consider:

a)

Thus,          
          
E(x) = Expected value = mean =    6.134 [ANSWER]

b)

Var(x) = E(x^2) - E(x)^2 =    1.098044      

Thus,

s(x) = sqrt [Var(x)] =    1.047875947 [ANSWER]

c)

NO, becasue the probability of winning in four games is greater than 0.05.

x P(x) x P(x) x^2 P(x) 4 0.1019 0.4076 1.6304 5 0.1853 0.9265 4.6325 6 0.1897 1.1382 6.8292 7 0.5231 3.6617 25.6319

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