Question

In: Statistics and Probability

44​% of men consider themselves professional baseball fans. You randomly select 10 men and ask each...

44​% 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.) ​(b) ​P(xgreater than or equals​6)equals nothing ​(Round to three decimal places as​ needed.) ​(c) ​P(xless than​4)equals nothing ​(Round to three decimal places as​ needed.)

Solutions

Expert Solution

p = 0.44

n = 10

This is a binomial distribution.

P(X = x) = 10Cx * 0.44x * (1 - 0.44)10-x

a) P(X = 5) = 10C5 * 0.445 * 0.565 = 0.229

b) P(X > 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

                  = 10C6 * 0.446 * 0.564 + 10C7 * 0.447 * 0.563 + 10C8 * 0.448 * 0.562 + 10C9 * 0.449 * 0.561 + 10C10 * 0.4410 * 0.560

                  = 0.241

c) P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

                  = 10C0 * 0.440 * 0.5610 + 10C1 * 0.441 * 0.569 + 10C2 * 0.442 * 0.568 + 10C3 * 0.443 * 0.567

                  = 0.288


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