Mth562-HW7-3

Mth562-HW7-3 - MTH/STA 562 Exercise 7.22 . This is a random...

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Unformatted text preview: MTH/STA 562 Exercise 7.22 . This is a random sample of size n = 100 from a population with mean & = 14 and standard deviation = 2. By the Central Limit Theorem , ( a ) P n Y > 14 : 5 o & P ( Z > : 5 2 = p 100 ) = P f Z > 2 : 5 g = 0 : 0062 : ( b ) P (& & & & & Y 14 2 = p 100 & & & & & 1 : 96 ) & : 95 which implies that P n 13 : 608 Y 14 : 392 o & : 95 : Exercise 7.23 . This is a random sample of size n = 100 from a population with mean & and standard deviation = 2 : 5. By the Central Limit Theorem , P n& & & Y & & & & : 5 o & P ( j Z j : 5 2 : 5 = p 100 ) = P fj Z j 2 g = 1 2 P f Z > 2 g = 1 2 (0 : 0228) = 0 : 9544 : Exercise 7.24 . This is a random sample of size n from a population with mean & and standard deviation = 2 : 5. By the Central Limit Theorem , : 95 = P n& & & Y & & & & : 4 o & P ( j Z j : 4 2 : 5 = p n ) = 1 2 P ( Z > : 4 2 : 5 = p n ) or P ( Z > : 4 2 : 5 = p n ) = 0 : 025 : Thus, : 4 2 : 5 = p n = 1 : 96 or n = 150 : 0625 : That is, n = 151 men should be chosen. Exercise 7.25 . This is a random sample of size n = 64 from a population with mean & = $5 : 00 and standard deviation = $0 : 50. By the Central Limit Theorem , P n Y & 6 : 90 o P ( Z & 6 : 90 7 : 00 : 50 = p 64 ) = P f Z & 1 : 6 g = 0 : 0548 : Exercise 7.26 . This is a random sample of size n = 40 from a population with mean & and standard deviation range 4 = 3 4 = 0 : 75. By the Central Limit Theorem , P n& & & Y & & & & & : 2 o P ( j Z j & : 2 : 75 = p 40 ) = P fj Z j & 1 : 69 g = 1 2 P f Z > 1 : 69 g = 1 2 (0 : 0455) = 0 : 9090 : Exercise 7.27 . This is a random sample of size n from a population with mean & and standard deviation : 75. By the Central Limit Theorem , : 90 = P n& & & Y & & & & & : 1 o P ( j Z j & : 1 : 75 = p n ) = 1 2 P ( Z > : 1 : 75 = p n ) or P ( Z > : 1 : 75 = p n ) = 0 : 05 : Thus, : 1 : 75 = p n = 1 : 645 or n = 152 : 21 : That is, at least n = 153 core samples should be taken....
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Mth562-HW7-3 - MTH/STA 562 Exercise 7.22 . This is a random...

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