A grocery store refrigerator contains 60 cartons of eggs. Of these, 40 cartons a

Question

A grocery store refrigerator contains 60 cartons of eggs. Of these, 40 cartons are fully intact while the rest contain at least one broken egg. A sample of 11 cartons will be selected (without replacement) from the 60 cartons in the refrigerator. Let X = number of cartons in the sample that are fully intact.

A grocery store refrigerator contains 60 cartons of eggs. Of these, 40 cartons are fully intact while the rest contain at least one broken egg. A sample of 11 cartons will be selected (without replacement) from the 60 cartons in the refrigerator. Let X = number of cartons in the sample that are fully intact. (a) The probability that the sample will contain exactly 8 cartons that are fully intact is (b) The expected value of X is (c) The variance of X is

Explanation / Answer

This is hypergeomteric distribution.

N = 60

k = 40

n = 11

a) P(X = 8) = 40C8 * 20C3 / 60C11 = 76904685 * 1140 / 342700125300 = 0.2558

b) Expected value = n * k / N = 11 * 40 / 60 = 7.33 or 7 (approximately)

c) Variance = n * k * ( N - k ) * ( N - n ) / [ N2 * ( N - 1 ) ] = 11 * 40 * ( 60 - 40 ) * ( 60 - 11 ) / [ 602 * ( 60 - 1 ) ] = 2.03 or 2 (approximately)

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