Adjusted Gross Incomes. The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 4.16 show a frequency distribution (number of returns) for adjusted gross income (AGI) from federal individual income tax returns, where K = thousand.

TABLE 4.16 Adjusted gross incomes Adjusted Frequency gross income (1000s) Event Probability Under $10K 26,268 A

$10K–under $20K 22,778 B

$20K–under $30K 18,610 C

$30K–under $40K 14,554 D

$40K–under $50K 11,087 E

$50K–under $100K 30,926 F

$100K & over 18,227 G 142,450 A federal individual income tax return is selected at random.

a. Determine P(A), the probability that the return selected shows an AGI under $10K.

b. Find the probability that the return selected shows an AGI between $30K and $100K (i.e., at least $30K but less than $100K).

c. Compute the probability of each of the seven events in the third column of Table 4.16, and record those probabilities in the fourth column.