One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 5 will need an audit?

A. 0.9998

B. 0.0109

C. 0.0002

D. 0.9999

Answer:

option is A

A. 0.9998

Step-by-step explanation

??Here Each of the trials is independent. Each trial have absolutely no effect on any of the others, which means we will use Binomial distribution???Use Binomial distribution formula??

P(x)=?n??C?x??⋅p?x??⋅(1−p)?n−x????

Here ?n??C?x??=C(n,x) 

stands for combination, given by formula C(n,x)=???n!/x!(n−x)!

????Where

??p=Probability of a success on an individual trial??

n = number of trials????

One out of every 92 tax returns that a tax auditor examines requires an audit.

Hence P(Audit) = 1/92

If 50 returns are selected at random, hence n =50

 probability that less than 5 will need an audit = P(0) +P(1) +P(2) + P(3) +P(4)

=?(?50?/0??)(???1/92??)?0??(1−???1/92??)?50??+(?50/?1??)(???1/92??)?1??(1−???1/92??)?40??+? ?(?50/?2??)(???1/92??)?2??(1−???1/92??)?48??+(?50?/3??)(??1/92??)?3??(1−???1/92??)?47??+(?50?/4??)(???1/92??)?4??(1−???1/92??)?46???

=0.9998