FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 10.19Calculation of expected trequencies
x Frequency (NP(x))
0 NP(0) = 0 1211 NP(0)×= ×=m 1 121.3 .5 60.65 612 NP(1)×= =m 22 60.65 .5× 15.16 153 NP(2)×= =m 33 15.16 .5× 2.53 34 NP(3)×= =m 44 2.53 .5× .29 0
Total 20010.4 NORMAL DISTRIBUTIONThe Binomial distribution and Poisson distribution discussed above are discrete probability distributions. The
normal distribution is highly useful in the field of statistics and is an important continuous probability
distribution. The graph of this distribution is called normal curve, a bell-shaped curve extending in both the
directions, arriving nearer and nearer to the horizontal axis but never touches it.
The normal distribution was first discovered by the English mathematician De-Moivre (1667-1754) in 1673 to
solve the problems in game of chances. Later, it was applied in natural and social science by the French
mathematician La Place (1749-1827). Normal distribution is also known as Gaussian distribution (Gaussian
Law of Error).
In binomial distribution, which is a discrete distribution as the expression of N(p + q)n gives the expected
frequencies of 0, 1, 2, 3..N successes. As n gets very large, the problem of computing the frequencies
becomes difficult and tedious. This difficult situation is handled by the application of normal curve. This
curve not only eliminates tedious computations but also gives close approximation to binomial distribution.
The following illustrations will clear the point.
Example 21 :
We know that when an unbiased coin is tossed 10 times, the probability of getting x heads is:
()! ()()^10
()!!
px n p qrx
nxx= −
−
x can be 0, 1, 2, 3...10