Normal approximation to binomial distribution
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It is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are
a) less than 120 yellow beans
b) between 120 and 150 yellow beans (inclusive)
c) more than 160 yellow beans
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Solution Summary
The solution discusses that it is known that in a sack of mixed bean seeds, 35% are yellow beans. Use the normal approximation to the binomial distribution to find the probability that in a sample of 400 beans there are
a) less than 120 yellow beans
b) between 120 and 150 yellow beans (inclusive)
c) more than 160 yellow beans
Solution Preview
Let X be the no. of yellow beans
X ~ Bin (400, 0.35)
Since n is large, p is not too small, such that
np = 140
npq = 260
We use normal approximation to binomial distribution.
Therefore X~N (140, 91) approx Note: X~N (np, npq)
a) P(x < 120) = P(x < 119.5)
...
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