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Chapter 09

# Chapter 09 - 151 Chapter 9 9.1 a b c d 1/6 9.2 a 3 = X P...

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151 Chapter 9 9.1 a, b, c, & d 1/6 9.2 a ) 3 ( = X P =P(1,5) + P(2,4) + P(3,3) + P(4,2) + P(5,1) = 5(1/36) = 5/36 b ) 4 ( = X P =P(2,6) + P(3,5) + P(4,4) + P(5,3) + P(6,2) = 5(1/36) = 5/36 c ) 1 ( = X P =P(1,1)= 1/36 d ) 6 ( = X P = P(6,6) = 1/36 9.3 Var ( X ) < Var (X) 9.4 a P( X = 1) = (1/6) 5 = .0001286 b P( X = 6) = (1/6) 5 = .0001286 9.5 The sampling distribution of the mean is normal with a mean of 40 and a standard deviation of 12/ 100 = 1.2. 9.6 No because of the central limit theorem. 9.7 a ) 1050 ( > X P = ÷ ÷ø ö ç çè æ - > s m - 16 / 200 1000 1050 / n X P = P(Z > 1.00) = .5 ° P(0 < Z < 1.00) = .5 - .3413 = .1587 b = < ) 960 (X P ÷ ÷ø ö ç çè æ - < s m - 16 / 200 1000 960 / n X P = P(Z < -.80) = .5 ° P(0 < Z < .80) = .5 - .2881 = .2119 c = > ) 1100 (X P ÷ ÷ø ö ç çè æ - > s m - 16 / 200 1000 1100 / n X P = P(Z > 2.00) = .5 ° P(0 < Z < 2.00) = .5 - .4772 = .0228 9.8 a ) 1050 ( > X P = ÷ ÷ø ö ç çè æ - > s m - 25 / 200 1000 1050 / n X

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P = P(Z > 1.25) = .5 ° P(0 < Z < 1.25) = .5 - .3944 = .1056 b = < ) 960 (X P ÷ ÷ø ö ç çè æ - < s m - 25 / 200 1000 960 / n X P = P(Z < -1.00) = .5 ° P(0 < Z < 1.00) 152 = .5 - .3413 = .1587 c = > ) 1100 (X P ÷ ÷ø ö ç çè æ - > s m - 25 / 200 1000 1100 / n X P = P(Z > 2.50) = .5 ° P(0 < Z < 2.50) = .5 - .4938 = .0062 9.9 a ) 1050 ( > X P = ÷ ÷ø ö ç çè æ - > s m - 100 / 200 1000 1050 / n X P = P(Z > 2.50) = .5 ° P(0 < Z < 2.50) = .5 - .4938 = .0062 b = < ) 960 (X P ÷ ÷ø ö ç çè æ - < s m - 100 / 200 1000 960 / n X P = P(Z < -2.00) = .5 ° P(0 < Z < 2.00) = .5 - .4772 = .0228 c = > ) 1100 (X P ÷ ÷ø ö ç çè æ - > s m - 100 / 200
1000 1100 / n X P = P(Z > 5.00) = 0 9.10 a = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 4 / 5 50 52 / 4 / 5 50 49 n X P = P(-.40 < Z < .80) = P(0 < Z < .40) + P(0 < Z < .80) = .1554 + .2881 = .4435 b = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 16 / 5 50 52 / 16 / 5 50 49 n X P = P(-.80 < Z < 1.60) = P(0 < Z < .80) + P(0 < Z < 1.60) = .2881 + .4452 = .7333 c = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 25 / 5 50 52 / 25 / 5 50 49 n X P = P(-1.00 < Z < 2.00) = P(0 < Z < 1.00) + P(0 < Z < 2.00) = .3413 + .4772 = .8185 9.11 a = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 4 / 10 50 52 / 4 / 10 50 49 n X P = P(-.20 < Z < .40)

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= P(0 < Z < .20) + P(0 < Z < .40) = .0793 + .1554 = .2347 b = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 16 / 10 50 52 / 16 / 10 50 49 n X P = P(-.40 < Z < .80) = P(0 < Z < .40) + P(0 < Z < .80) = .1554 + .2881 = .4435 c = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 25 / 10 50 52 / 25 / 10 50 49 n X P = P(-.50 < Z < 1.00) = P(0 < Z < .50) + P(0 < Z < 1.00) = .1915 + .3413 = .5328 153 9.12 a = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 4 / 20 50 52 / 4 / 20 50 49 n X P = P(-.10 < Z < .20) = P(0 < Z < .10) + P(0 < Z < .20) = .0398 + .0793 = .1191 b = < < ) 52 49 ( X P ÷ ÷ø ö ç çè æ - < s m - < - 16 / 20 50 52 / 16 / 20 50 49 n X P = P(-.20 < Z < .40) = P(0 < Z < .20) + P(0 < Z < .40) = .0793 + .1554 = .2347
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Chapter 09 - 151 Chapter 9 9.1 a b c d 1/6 9.2 a 3 = X P...

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