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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

Respuesta :

MathPhys

Answer:

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

The probability should be option B. 0.0028

Calculation of the probability:

It is the binomial distribution.

Now

The mean and standard deviation should be

[tex]\mu[/tex] = np = (0.02) (1500) = 30

= 5.42

[tex]\sigma = \sqrt(npq) = \sqrt (0.02 \times 0.98 \times 1500)[/tex]

Now we determine the z-score:

[tex]z = (x - \mu) \div \sigma\\\\z = (45 - 30) \div 5.42[/tex]

z = 2.77

Now here we use a z-score table

So,

P(z > 2.77) = 1 − P(z < 2.77)

P(z > 2.77) = 1 − 0.9972

P(z > 2.77) = 0.0028

learn more about the probability here: https://brainly.com/question/24164645

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