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Unformatted text preview: STAT 420 Spring 2010 Homework #1 (12 points) (due Friday, January 29, by 4:00 p.m.) 1. 2.70 A company has found that the length of time a newly hired agent stays with the company is approximately normally distributed with mean 18 months and standard deviation 3 months. = 18 months, = 3 months. 2 years = 24 months. a) Find the probability that a newly hired agent will stay with the company at least two years. P ( X 24 ) =  3 18 24 Z P = P ( Z 2.00 ) = 0.0228 . b) What is the probability that two new agents hired independently will both stay with the company at least two years? P ( both stay ) = P ( 1st stays AND 2nd stays ) = P ( 1st stays 2nd stays ) by independence = P ( 1st stays ) P ( 2nd stays ) = 0.0228 0.0228 0.00052 . c) What is the probability that the average length of stay of the two agents is greater than two years? P ( X 24 ) =  2 3 18 24 Z P = P ( Z 2.83 ) = 0.0023 . OR P ( 2 X X 2 1 + 24 ) = P ( X 1 + X 2 48 ) = + 9 9 2 18 48 Z P =  18 36 48 Z P = P ( Z 2.83 ) = 0.0023 . 2. 3.5 The salary of junior executives in a large retailing firm is normally distributed with standard deviation = $1,500. If a random sample of 25 junior executives yields an average salary of $16,400, what is the 95percent confidence interval for , the average salary of all junior executives. = $1,500, n = 25, X = $16,400. n z 2 X 95% confidence, = 0.05, z 0.025 = 1.960. 25 500 , 1 960 . 1 400 , 16 16,400 588 ( 15,812 , 16,988 ) 3. 3.12 Redo Problem 3.5 without assuming that the population standard deviation is known. You are given s = $1,575. s = $1,575, n = 25, X = $16,400. ( 29 n t n s 1 2 X 95% confidence, = 0.05, t 0.025 ( 24 ) = 2.064. 25 575 , 1 064 . 2 400 , 16 16,400 650.16 ( 15,749.84 , 17,050.16 ) 4. A store sells "16ounce" boxes of Captain Crisp cereal. A random sample of 9 boxes was taken and weighed. The results were the following (in ounces):...
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This note was uploaded on 04/08/2012 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Stepanov

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