Question 1194452: In many situations, the normal distribution can be used to approximate the binomial distribution.
a)Explain the conditions in which this can be done, and explain why we might take advantage of this property.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If there are two outcomes with constant probability
if np and n(1-p) are > 5 (some use 10)
Do this where large factorials might occur and cannot be calculated.
A batter is hitting 0.400. In the next 200 at bats, what is the chance of his getting 90 or more hits.
With the binomial, this is 200C50 *0.4^90*0.6^110, and that is only for 90 hits. One has to calculate 91, 92,
Normal approximation np=80 (mean)
np(1-p)=80*0.6=48 (variance)
sqrt 48 is 6.93
want z>(89.5-80)/6.83, and that is a lot easier to do.
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