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21 August, 05:14

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

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Answers (1)
  1. 21 August, 08:41
    0
    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
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