Paper 4: Fundamentals of Business Mathematics & Statistic

10.10 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Theoretical Distribution

(b) probability of atleast 2 heads = l – P(0)+P(l)

=

12 12 12 12

01

1 11

CC 22

−+⎛⎞ ⎛⎞⎜⎜⎟⎟⎟⎟

⎜⎜⎜⎜⎝⎠ ⎝⎠⎟⎟⎟⎟

=^1 −=4096 409613 4083

... The number of occasions of getting at least 2 heads in

4096 4083

×= 4096 4083times

4096 tosses

(c) Probability of 6 heads:

P(6) =

12 12

6

1

C 2

⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

= 4096924

The number of occasions of getting exactly 6 heads =

4096 924

× 4096

= 924 times

Example 9 :

The mean, of a binomial distribution is 20 and standard deviation is 4. Find out n, p and q.

Solution:

Mean = 20 (np)

Standard Deviation = 4

npq = 4

npq = 16

q =

(^16) or 0.8
20
npq
np =
p = 1 – 0.8 = .2
n = 0.2^20 =^100
Example 10 :
Obtain the binomial distribution for which mean is 10 and the variance is 5.
Solution :
The mean of binomial distribution m=np= 10
The variance= npq = 5