NORMAL APPROXIMATION OF THE BINOMIAL DISTRIBUTION

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NORMAL APPROXIMATION OF THE BINOMIAL DISTRIBUTION
When n is large you cant use tables for the
Binomial and manually calculating probabilities
is tedious
The Normal distribution is a continuous
distribution and the Binomial distribution is a
discrete distribution, however with a Continuity
Correction we can use the Normal distribution to
approximate the Binomial distribution (nb. the
normal is easier and quicker to use!)
If tell someone your height to the nearest cm
(discrete) and it is 156cm then the upper and
lower bounds that it actually could be are
155.5cm and 156.5cm
As there is no probability for exact values in a
continuous distribution you cannot find the
P(X156) but you can find the P(155.5ltXlt156.5)
0.5 Continuity Correction
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NOT AS SIMPLE AS IT SEEMS!
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ONCE YOU CAN DO A CONTINUITY CORRECTION THE REST
IS EASY!
If X Bin (n, p) then E(X) np, Var(X)
npq Then if n is large and p is neither too
large or too small (npgt5 and nqgt5) X N(np,
npq) approximately.
Example Find the probability of obtaining
between 4 and 7 heads inclusive with 12 tosses of
a fair coin, (a) using the normal approx. to the
bin (b) using the binomial distribution
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X Bin (12, 0.5)
B) From binomial distribution