Question

Approximate the probability that X is greater than 70 and less than 90.

Answer 1

The probability that X is greater than 70 and less than 90 is; 0.85

How to find the probability?

Let X be the binomial random variable with the parameters:

n = 200

p = 0.4

Then, the random variable Z defined as:

Z = (X - np)/(√(np(1 - p)

The probability that X is greater than 70 and less than 90 is expressed as; P(70 < X < 90)

At X = 70, we have;

Z = (70 - (200*0.4))/(√(200 * 0.4(1 - 0.4))

Z = -1.44

At X = 90, we have;

Z = (90 - (200*0.4))/(√(200 * 0.4(1 - 0.4))

Z = 1.44

Thus, the probability would be expressed as;

P(-1.44 < Z < 1.44)

From online p-value calculator, we have;

P(-1.44 < Z < 1.44) = 0.85

Complete question is;

Suppose that X is a binomial random variable with n = 200 and p = 0.4 Approximate the probability that X is greater than 70 and less than 90.

Read more about probability at; brainly.com/question/4621112

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