A bank found that 25% of its loans to new small businesses become delinquent. If 500 small businesses are selected randomly from the banks files, what is the probability that at least 130 of them are delinquent? Compare the result from the normal approximation with that from a calculation using the binomial distribution?

Question

anonymous · Answer

How can you solve without using a graphing calculator?

anonymous · Answer

If the question asks exact 130 of them are delinquent, then we can use the binomial distribution, ie
P (130) = (500C130) (.25^130) (.75^370)
Since the question asks at least 130, We need to use summation formula
P (x >=130) = (Sigma for x from 130 to 500) (500 C x) (.25 ^ x) (.75^ 500-x)
We don't need a graphing calculator, but we do need a calculator that can do the Sigma.