A law enforcement agency processes 500 background checks for rearms purchasers. Fifty applicants are convicted felons. Through a clerk's error, 10 applicants are approved without checking for felony convictions.
(a) Justify the use of the binomial approximation.
(b) What is the probability that none of the 10 is a felon?
(c) That at least two of the 10 are convicted felons?
(d) That fewer than 4 of the 10 are convicted felons?