Applied Statistics and Probability for Engineers

3-8 HYPERGEOMETRIC DISTRIBUTION 85

012345

0.0

0.1

0.3

0.4

0.5

f (x)

0.2

N

10

50

50

n

5

5

0.6 5

0.7 K

5

25

3

0.8

x

Figure 3-12 Hypergeometric distributions for

selected values of parameters N,K, and n.

and the number of successes available, K. Also, if at least suc-

cesses must occur in the sample. Selected hypergeometric distributions are illustrated in

Fig. 3-12.

EXAMPLE 3-26 The example at the start of this section can be reanalyzed by using the general expression in

the definition of a hypergeometric random variable. That is,

EXAMPLE 3-27 A batch of parts contains 100 parts from a local supplier of tubing and 200 parts from a sup-

plier of tubing in the next state. If four parts are selected randomly and without replacement,

what is the probability they are all from the local supplier?

P 1 X 22 

a

50

2

b a

800

0

b

a

850

2

b



1225

360825

0.003

P 1 X 12 

a

50

1

b a

800

1

b

a

850

2

b



40000

360825

0.111

P 1 X 02 

a

50

0

b a

800

2

b

a

850

2

b



319600

360825

0.886

n KN, n KN

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