10.20 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSTheoretical Distribution
No. of heads (x) Probability p(x)
0 1/1024 = 0.0097
1 10/1024 = 0.0098
2 45/1024 =0.0439
3 120/1024 = 0.1172
4 210/1024 =0.2051
5 252/1024 = 0.2461
6 210/1024 = 0.2051
7 120/1024 = 0.1171
8 45/1020 = 0.0439
9 10/1024 = 0.0098
10 1/1024 = 0.0097P(x) = nCxpxqn-x
Wen may now draw a histogram of the probability distribution, using class frequencies –^12 to –^12 , 21 to 1^12 ,
121 to 2^12 ...... 9^12 to 10 21.It may be noted that the above figure is symmetrical and bell shaped. It is symmetrical due to the fact, p
= q, when p is not equal to q, the distribution tends to the form of the normal curve, when n becomes
large.
A normal distribution is determined by the parameters-mean and standard deviation. For different values
of mean and standard deviation, we get different normal distributions. The area under the normal curve is
always taken as unity so as to represent total probability. The area is of great importance in a variety of
problems because such an area represents frequency.