Question

The chances of a tax return being audited are about 22 in 1,000 if an income is less than​$100,000 and 31 in 1,000

if an income is​ $100,000 or more. Complete parts a through e.

a. What is the probability that a taxpayer with income less than​ $100,000 will be​ audited? With income of​ $100,000 or​ more?

P(taxpayer with income less than $100,000 is audited)=_____________(Type an integer or a​ decimal.)

What is the probability that a taxpayer with income of​ $100,000 or more will be​ audited P(taxpayer with income of $100,000 or higher is audited)=___________​(Type an integer or a​ decimal.)

b. If five taxpayers with incomes under​ $100,000 are randomly​ selected, what is the probability that exactly one will be​ audited? That more than one will be​ audited?

P(x=1)=__________​(Round to four decimal places as​ needed.)

What is the probability that more than one will be​ audited?

P(x>1)=_____________(Round to four decimal places as​ needed.)c. Repeat part b assuming that

five taxpayers with incomes of​ $100,000 or more are randomly selected.

P(x=1)=____________​(Round to four decimal places as​ needed.)

What is the probability that more than one will be​ audited?

P(x>1)=______________​(Round to four decimal places as​ needed.)

d. If two taxpayers with incomes under​ $100,000 are randomly selected and two with incomes more than​ $100,000 are randomly​ selected, what is the probability that none of these taxpayers will be​ audited?

​P(none of the taxpayers will be ​audited)=___________________​(Round to four decimal places as​ needed.)

e. What assumptions did you have to make in order to answer these​ questions?

A.We must assume that the variables are random variables. We must assume that the trials are​ identical, and the probability of success varies from trial to trial.

B.We must assume that the variables are binomial random variables. We must assume that the trials are identical and dependent.

C.We must assume that the variables are binomial random variables. We must assume that the trials are​ identical, the probability of success is the same from trial to​ trial, and that the trials are independent.

D.We must assume that the variables are binomial random variables. We must assume that the trials are​ identical, the probability of success varies from trial to​trial, and that the trials are dependent.

Answer 1