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