Question

CO 4) 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 2 will need an audit?

Answer 1

Given,

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

i.e. Probability of a tax return that a tax auditor examines requires an audit : p= 1/92 = 0.01087

q = 1-p = 1-0.01087= 0.98913

n : number of returns that are selected at random = 50

X : Number of returns that will need an audit

X follows a Binomial distribution with p :0.01087 and n: 50 and the probability mass function given by

probability that less than 2 will need an audit = P(X<2) = P(X=0) + P(X=1)

P(X<2) = P(X=0) + P(X=1) = 0.57899+0.31814 = 0.89713

Probability that less than 2 will need an audit = 0.89713

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Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function