Here is the distribution of the adjusted gross income (in thousands of dollars)

Question

Here is the distribution of the adjusted gross income (in thousands of dollars) reported on individual federal income tax returns in a particular year. (Round your answers to three decimal places.)

(a) What is the probability that a randomly chosen return shows an adjusted gross income of $30,000 or more?

(b) Given that a return shows an income of at least $30,000, what is the conditional probability that the income is at least $100,000?

*Only need part b.

Explanation / Answer

let us assume you have 100 people who follow the expected statistics.

38 of those people will have income 30-99
10 of those people will have income >100

so 48 of the 100 people have incomes > 30 p = 0.48

48 of the people have incomes >30 (given)
of those 10 have income >100

so 10 out of 27 have income >100 p = 10/48 = 0.208

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