Question

5959​%

of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

​(a)

​P(5)equals=nothing

​(Round to three decimal places as​ needed.)

Answer 1

59​% of men consider themselves professional baseball fans. This means that the probability that a randomly selected man considers himself a professional baseball fan is 0.59

Let X be the number out of 10 randomly selected men, who consider themselves professional baseball fans. We can say that X has a Binomial distribution with parameters, number of trials n=10 and success probability (the probability that a randomly selected man considers himself a professional baseball fan) p=0.59

The Binomial probability of X=x out of 10 randomly selected men consider themselves professional baseball fans is

a) the probability that the number who consider themselves baseball fans is​ exactly​ five is

ans: the probability that the number who consider themselves baseball fans is​ exactly​ five is 0.209

b) the probability that the number who consider themselves baseball fans is​ at least​ six ( 6 or more) is

ans: the probability that the number who consider themselves baseball fans is​ at least​ six is 0.608

c) the probability that the number who consider themselves baseball fans is​ less than four is

ans: the probability that the number who consider themselves baseball fans is​ less than four is 0.063