Explore BrainMass

# Normal approximation to binomial distribution

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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

https://brainmass.com/statistics/probability/normal-approximation-binomial-distribution-10714

#### 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)

...

#### 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

\$2.49