4848 % 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.

Given the information, we shall proceed as follows:

The given problem is a binomial problem.

n=10 and p=0.48

thus, the probability that the number who consider themselves baseball fans is:

a] exactly five

P (x=5) = 10C5 (0.48) ^5 (0.52) ^5=0.244

b] at least 6

P (x>=6) = 1-P (x<8)

=P (6) + P (7) + P (8) + P (9) + P (10)

=10C6 (0.48) ^6 (0.52) ^4+10C7 (0.48) ^7 (0.52) ^3+10C8 (0.48) ^8 (0.52) ^2+10C9 (0.48) ^9 (0.52) ^1+10C10 (0.48) ^10

=0.1878+0.0991+0.0343+0.0070+0.0007

=0.3289

The answer: 0.3289

c] Less than 6

P (x=6)

=1-0.3289

=0.6711