Question

4. According to government data, the probability that an adult was never in a museum is 18%. In a random survey of 15 adults, what is the probability that two or fewer were never in a museum? Round the answer to 4 decimal places. (3pts)

Answer 1

X ~ Bin ( n , p)

Where n = 15 , p = 0.18

Binomial probability distribution is

P(X) = nCx * px * ( 1 - p)n-x

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 15C0 * 0.180 * ( 1 - 0.18)15 + 15C1 * 0.181 * ( 1 - 0.18)14 + 15C2 * 0.182 * ( 1 - 0.18)13

= 0.4766