About 2% of the worlds population have gray eyes. What is the probability that in a random sample of 1,500 people, more than 45 of them has gray eyes?

A. 1

B. 0.0028

C. 0.02

D. 0.9972

E. 0.98

B. 0.0028

Step-by-step explanation:

This is a binomial distribution. We could use a calculator to find the probability, or, since the sample size is large enough and both np and nq are larger than 10, we can approximate this as a normal distribution.

To do so, we first find the mean and standard deviation.

μ = np = (0.02) (1500) = 30

σ = √ (npq) = √ (0.02 * 0.98 * 1500) = 5.42

Now we find the z-score:

z = (x - μ) / σ

z = (45 - 30) / 5.42

z = 2.77

Finally, we use a z-score table to find the probability.

P (z > 2.77) = 1 - P (z < 2.77)

P (z > 2.77) = 1 - 0.9972

P (z > 2.77) = 0.0028