About 81% of the world's population can roll their tongue. What is the probability that in a random sample of 2,000 people, more than 1,600 of them can roll their tongue?

A. 0.8729

B. 0

C. 1

D. 0.1271

E. 0.19

A. 0.8729

Step-by-step explanation:

Since the sample size is large enough (np > 10 and nq > 10), we can estimate this with a normal distribution.

μ = p

μ = 0.81

σ = √ (pq / n)

σ = √ (0.81 (1 - 0.81) / 2000)

σ = 0.0088

x = 1600 / 2000

x = 0.8

Find the z score:

z = (x - μ) / σ

z = (0.8 - 0.81) / 0.0088

z = - 1.14

Use a calculator or table to find the probability.

P (Z > - 1.14)

1 - P (Z < - 1.14)

1 - 0.1271

0.8729