Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.11

... q =

(^5) 0.5
10
npq
np ==
p = 1 – q i.e., 1 – 0 = 0.5
... np = 10 i.e., n × 0.5 = 10
n = 0.5^10 =^20
Therefore the required binomial distribution is
(p + q)n = (0.5 + 0.5)^20 or

1120

22

⎛⎞⎜ + ⎟⎟

⎜⎜⎝⎠⎟⎟

Example 11 :

Obtain the binomial distribution for which the mean is 20 and the variance is 15.

Solution :

The variance= npq = 15

Mean = np = 20

... q =

15 3

20 4

npq

np ==

... q =^1 −=^3144

np = 20

i.e. n× 41 = 20

... n = 1/ 420 20 4== 1 ×^80

The binomial distribution is :

(p + q)n =

1380

44

⎛⎞⎜ + ⎟⎟

⎜⎜⎝⎠⎟⎟

Fitting of Binomial Distribution
The probability of 0, 1, 2, 3 success would be obtained by the expansion of (q+ p)n. Suppose this experiment
is repeated for N times, then the frequency of r success is;

N × P(r) = N × nCrqn–r pr