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18 May, 14:14

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.

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  1. 18 May, 14:18
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    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
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