# 400Hw07 - STAT 400 Spring 2011 Homework #7 (due Friday,...

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STAT 400 Spring 2011 Homework #7 (due Friday, March 11, by 3:00 p.m.) From the textbook: 8th edition ( ) 1. 3.5-2 ( ) 2. 3.5-8 ( ) 3. 10.5-2 ( ) 4. 3.6-6 ( ) 5. 3.6-14 ( ) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ NOT from the textbook: 6. In Neverland, annual income is normally distributed with mean \$47,500 and standard deviation \$12,500. Neverland's IRS divides everyone into three groups: "low income" (below \$40,000), "middle income" (between \$40,000 and \$60,000), and "high income" (over \$60,000). Every year, the IRS audits 1% of the individuals in the "low income" group, 2.5% of the individuals in the "middle income" group, and 7% of the individuals in the "high income" group. Suppose that the individuals to be audited at selected at random. a) What proportion of Neverland's population falls into each of the three income groups? [ “Hint”: The answers should add up to 100%. ] b) What proportion of Neverland's population was audited last year? c) Suppose Mr. Smith was audited last year. What is the probability that Mr. Smith is in "low income" group? "Middle income" group? "High income" group? [ “Hint”: The answers should add up to 100%. ] d) Suppose Mr. Jones is not in the "low income" group. What is the probability that Mr. Jones will be audited this year? e)

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## This note was uploaded on 10/19/2011 for the course CS 231 taught by Professor - during the Spring '08 term at University of Illinois at Urbana–Champaign.

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400Hw07 - STAT 400 Spring 2011 Homework #7 (due Friday,...

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