Paper 4: Fundamentals of Business Mathematics & Statistic

10.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Theoretical Distribution

5511551

() 22 2

xx

pX CxxC

⎛⎞⎛⎞ ⎛⎞−

==⎜⎜ ⎜⎜⎜ ⎜⎟⎟ ⎟⎟⎟ ⎟⎟⎟ ⎟

⎜⎜ ⎜⎝⎠⎝⎠ ⎝⎠⎟⎟ ⎟

Number of heads (X)f(x) = 3,200 ×

5 15

Cx 2

⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

0

5 5

0

(0) 3,200^1100

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

1

5

(1) 3,200^511500

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

2

5 5

2

(2) 3,200^11000

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

3

5

(3) 3,200^5311000

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

4

5 5

4

(4) 3,200^1500

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

5

5 5

5

(5) 3,200^1100

fC 2

=× =⎛⎞⎜ ⎟⎟

⎜⎜⎝⎠⎟⎟

Total 3,200

Example 5 :

A box contains 100 transistors, 20 out of which are defective, 10 are selected for inspection. Indicate what

is the probability that

(i) all 10 are defective,

(ii) all 10 are good,

(iii) at least one is defective , and

(iv) at the most 3 are defective?

Solution:

Let ‘X’ represent the number of defective transistors selected. Then the possible values of ‘X’ are 1, 2, 3, ....,

10.

Now

p = p( transistor is defective)

===−=100 520 1;1q 5 51 4

Using formula for binomial distribution, the probability of X defective transistors is