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