This is hypergeometric distribution. Please calculate the following. (Please ans

Question

This is hypergeometric distribution. Please calculate the following. (Please answer all parts if not, please skip.)

4. A lot of 12 television sets includes three that are defective. Three of the sets are shipped to a hotel. a). Find the pmf for the number of defective TV's shipped to the hotel. b). Find the probability that at least one defective TV'S are shipped to the hotel. c). Find the probability that at most one defective TV'S are shipped to the hotel d). How many defective sets can the hotel expect? e). what is the variance?

Explanation / Answer

N = 12

k = 3

n = 3

a) P(X = x) = [ kCx ] [ N-kCn-x ] / [ NCn ] = [ 3Cx ] [ 9C3-x ] / [ 12C3 ]

b) P(X > 1) = 1 - P(X = 0) = 1 - [ 3C0 ] [ 9C3 ] / [ 12C3 ] = 1 - 0.3818 = 0.6182

c) P(X < 1) = P(X = 0) + P(X = 1)

= [ 3C0 ] [ 9C3 ] / [ 12C3 ] + [ 3C1 ] [ 9C2 ] / [ 12C3 ]

= 0.8727

d) Mean = n * k / N = 3 * 3 / 12 = 0.75 or 1 (approximately)

e) Variance = n * k * ( N - k ) * ( N - n ) / [ N2 * ( N - 1 ) ] = 3 * 3 * ( 12 - 3 ) * ( 12 - 3 ) / [ 122 * ( 12 - 1 ) ] = 0.46

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