Business Statistics

218 Business Statistics

Solution Probability of x successes in n trials is given by

( )

r N r

x n x

N

n

C C

P x

C

−

−

×

=

From the example, the following items are given:

N = 30 n = 4 r = 6

(a) No jar has less than 100 confectionery items

6 30 6

0 4 0

30

4

( 0)

C C

P x

C

−

−

×

= = =

0.3877

(b) Exactly three jars have less than 100 confectionery items

P(x = ) =

6 30 6

3 4 3

30

4

C C

C

−

−

×

= 0.0175

(c) Three or fewer jars have less than 100 confectionery items

P(x  ) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

=

6 30 6 6 30 6 6 30 6 6 30 6

0 4 0

1 4 1 2 4 2 3 4 3

30 30 30 30

4 4 4 4

C C C C C C C C

C C C C

− − − −

− − − −

× × × ×

+ + +

= 0.9994

(d) Three or more jars have less ...