Question

" C CELECOBOLI In Neverland, annual income (In $) is distributed according to Gamma distribution with a = 3 and 0 = $17,000. Every year, the IRS audits 1% of the Individuals with Income below $60,000, 3% of the individuals with income between $60,000 and $95,000, and 6% of the individuals with income above $95,000. Suppose that the individuals to be audited are selected at random. 150 50 100 income (in thousands $) a. What proportion of Neverland's population falls into each of the three income groups? That is, find P(X < $60,000), P($60,000 < X < $95,000), and P(x > $95,000). Round your answers to 4 decimal places. ["Hint": The answers should add up to 100%.] P(X < $60,000) = P($60,000 < X < $95,000) = P(X = $95,000) = e Tries 0/10 b. You have overheard Mr. Statman complain about being audited. What is the probability that Mr. Statman's income is below $60,000? Between $60,000 and $95,000? Above $95,000? Round your answers to 3 decimal places. ["Hint": The answers should add up to 100%.] P(X < $60,000 audit) = P($60,000 < X < $95,000 | audit) = P(X> $95,000 audit) = ETE* Tries 0/10

Answer 1

Given That :- 2:3 17.000 6% fep(x >95000) 1% fe* P(X<60000), 3% for P6000<x< 95000) a)op (x<$60,000) voing tueel function solver = GAMMADIST (X,«,, Cumulative) = GAMMA. DIST 60.000, 3, 17000, 1) = 0.6846 p(x < 20000) - 0.6846 iB) P/x560000 < X < 95000) : - P(X<95000) - P(x<60000) - GAMMA. DIST (95000, 3, 17000, 1) - GAMMA-DIST (60000, 3.17000, 1) = 0.9169 - 0.6846 = 0.2323 P (760000 < x <95000) - 0.2323 ii) P(x795000) - 1-PCX< 95000) = GAMMA. DIST (05000, 3, 17000, 1) - 0.9169 = 1-019169 = 0.0831 (x2 150cc), 0.083) b) PCX < 60000 (audit) :- Audit) -0.6346x0.01 + 0.2323 0 03 +0.08 31 X0-06 P(Audit)- 0.0188 0.6B46 XD-01 ) PCX < 60000 l audit) = -0.0188' = 0.3CM *) P (60000 < x <95000 landit ) - 0.2323 x0-03 0.371 0.088 iii) P(x 7 95000 laudit ) - 0.0831 x0.06 . 0.019 = 0.220