Question

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.)

Answer 1

p = 0.44

n = 10

This is a binomial distribution.

P(X = x) = 10Cx * 0.44^x * (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