# tut10ans - COMP211 Data and System Modeling (PROB/STAT)...

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COMP211 Data and System Modeling (PROB/STAT) Tutorial (Week 10) -Answer 1. a) Suppose that the average household income in some country is 900 coins, and the standard deviation is 200 coins. Assuming the Normal distribution of incomes, compute the proportion of “middle class”, whose income is between 600 and 1200 coins. Solution: For a Normal ( g = 900,G = 200 ) random variable X, ±²600 < ³ < 1200´ − ±² 600 − g G < ³ − g G < 1200 − g G ´ b) The government of the country in part (a) decides to issue food stamps to the poorest 3% of households. Below what income will families receive food stamps? Solution: We need to find such income x that P{X<x} = 3% = 0.03. This is an equation that can be solved in terms of x. Again, we standardize first, then use the table: ±²³ < µ´ = ± ¶· < ¸¹º » ¼ = Φ½ ¸¹º » ¾ = 0.03 , from where µ = g + GΦ ¹¿ (0.03) µ = g + G(−1.88) µ = 900 + (200)(−1.88) µ = ÀÁÂ coins 2. You wait for an elevator, whose capacity is 2000 pounds. The elevator comes with

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## This note was uploaded on 04/08/2012 for the course COMP 211 taught by Professor Dr.kwok during the Spring '12 term at Hong Kong Polytechnic University.

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tut10ans - COMP211 Data and System Modeling (PROB/STAT)...

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