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Unformatted text preview: ASW ESBE (5e) Chapter 7, Section 7.5 Solutions to Selected Problems 24. a. Show the sampling distribution of xbar (all values in dollars). 1. ( ) 4260 E x = 2. / 900/ 50 127.28 x n = = = 3. The sampling distribution of the sample mean is normal by CLT by CLT ( n = 50 > 30) b. Within $250 of Want Prob ( $250 xbar +$250) = Prob (4010 x 4510) 4510 4260 1.96 127.28 z = = Prob (4010 x 4510) = Prob (1.96 z 1.96) = Prob (z 1.96) Prob (z 1.96) = 0.9750 0.0250 = 0.9500 c. Within $100 Want Prob ( $100 xbar +$100) = Prob (4160 x 4360) 4360 4260 .79 127.28 z = = Prob (4160 x 4360) = Prob (0.79 z 0.79) = Prob (z 0.79) Prob (z 0.79) = 0.7852 0.2148 = 0.5704 Some Section 7.5 problem solutions 1 New question: Suppose a sample of size n = 50 was chosen. The sample mean xbar was calculated to be $4615. What is the chance of selecting a sample whose is $4615 or larger? Want Prob (xbar $4615) 79 . 2 28 . 127 $ 4260 $ 4615 $ = = = x x z Prob (xbar $4615) = Prob (z 2.79) = 1 Prob (z 2.79) = 1 0.9974 = 0.0026 Note: 0.0026 < 0.01, so xbar $4615 is a rare event. Possible explanations: 1. Bad luck. 2. Nonrandom sample. 3. Maybe 4260 as claimed, or 900 as claimed, or both. Some Section 7.5 problem solutions 2 25. Given: = 1020 = 100 n = 75 Show the sampling distribution of xbar. 1. E ( x ) = 1020 2. x n = = = / / . 100 75 1155 3. The sampling distribution of the sample mean is normal by CLT ( n = 75 > 30) b. Want Prob ( 10 xbar +10) = Prob (1010 xbar 1030) 1030 1020 .87 11.55 z = = 1010 1020 .87 11.55 z = =  Prob (1010 xbar 1030) = Prob (0.87 z 0.87) = Prob ( z 0.87) Prob (z 0.87) = 0.8078 0.1922 = 0.6156 c. Want Prob ( 20 xbar +20) = Prob (1000 xbar 1040) 1040 1020 1.73 11.55 z = = 1000 1020 1.73 11.55 z = =  Area = .4582 Prob (1000 xbar 1040) = Prob (1.73 z 1.73) = Prob ( z 1.73) Prob (z 1.73) = 0.9582 0.0418 = 0.9164 Some Section 7.5 problem solutions 3 New question: Suppose a sample of size n = 75 was chosen. The sample mean xbar was calculated to be 1050. What is the chance of selecting a sample whose is 1050 or larger? Want Prob (xbar 1050) 60 . 2 55 . 11 1020 1050 = = = x x z Prob (xbar 1050) = Prob (z 2.60) = 1 Prob (z 2.60) = 1 0.9953 = 0.0047 Note: 0.0047 < 0.01, so xbar 1050 is a rare event. Possible explanations: 1. Bad luck....
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This note was uploaded on 01/26/2011 for the course OM 210 taught by Professor Singer during the Fall '08 term at George Mason.
 Fall '08
 SINGER

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