Question

in a survey, 63% of americans said they own an anawering machine. If 12 Americans are selected at random, what is the probability that at least 10 own an answering machine.

Answer 1

X ~ Binomial (n,p)

Where n = 12 , p = 0.63

P(X) = ⁿC_x p^x ( 1 - p)^n-x

So,

P( X >= 10) = P (X = 10) + P (X = 11) + P (X = 12)

= ¹²C₁₀ 0.63¹⁰ 0.37² + ¹²C₁₁ 0.63¹¹ 0.37¹ + ¹²C₁₂ 0.63¹² 0.37⁰

= 0.1205