Question

44% of men have considered 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

Answer 1

X ~ Binomial (n,p)

Where n = 10 , p = 0.44

The binomial probability distribution is

P(X) = ⁿC_x p^x ( 1 - p)^n-x

a)

P( X = 5) = ¹⁰C₅ 0.44⁵ 0.56⁵

= 0.2289

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 0.56 +¹⁰C₁₀ 0.44¹⁰ 0.56⁰

= 0.2407

c)

P( X < 4) = P( X <= 3)

= 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

= 0.2877