Question

In the United States, 40% of the population have brown eyes (based on data from Dr. P. Sorita Soni at Indiana University). If 14 people are randomly selected, find the probability that at least 12of them have brown eyes.

Answer 1

0.0006087 (4 sf)

Explanation:

Binomial distribution: X ~ B(n, p)

where n is the number of trials and p is the probability of success

Let the random variable X be the number of people with brown eyes

n = 14

p = 40% = 0.4

Therefore, X ~ B(14, 0.4)

P(X ≥ 12) = 1 - P(X ≤ 11)

= 1 - 0.9993913226...

= 0.000608677...