Paper 4: Fundamentals of Business Mathematics & Statistic

10.18 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Theoretical Distribution

Solution:

Fitting Poisson Distribution

No. of Defective No. of Sets fx

0790

11818

224

313

400

N = 100 ∑=fx 25

.25

(1) (0)

(2) (1)

(3) (2)

(4) (3)

(^25) 0.25
100
0.779 (Given)
(0) 100 0.779 77.90
1 77.9 0.25 19.48
19.48 0.25 2.44
22
2.44 0.25 0.20
33
0.20 0.25 0.01
44
m

X

e

NP Ne

NP NP m

NP NP m

NP NP m

NP NP m

−

−

==

=

==×=

=×=×=

=×= ×=

=×=×=

=×=×=

Example 20 :

Fit a Poisson Distribution to the following data and calculate the theoretical frequencies :

x:01234

f: 123 59 14 3 1

Solution :

x01234

f (^123591431) ∑=f 200
fx 0 59 28 9 4 ∑=fx 100
Mean =^100200
= 0.5
NP(o) = Ne–m
= 200 ×e–5
= 200 ×.6065 = 121.3