Homework Solutions 07

# Homework Solutions 07 - (W4150 Intro to Probability and...

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Solutions to Homework #7 (W4150 ‘Intro to Probability and Statistics’, S04) Sec. 8.5. (1) P( μ x –1.9 σ x < X < μ x –.4 σ x ) = P( μ x –1.9 σ x - μ x < X - μ x < μ x –.4 σ x - μ x ) = P(-1.9 < (X - μ x )/ σ x < -.4) = P(z 1 = -1.9 < Z < -.4 = z 2 ) = .3446 - .0287 = .3159 Sec.8.5. (3) (a) for n = 64, σ x = σ / n = 5.6/8 = .7, whereas for n = 196, σ x = 5.6/14 = .4 the standard error of the mean is reduced from .7 to .4 when the sample size is increased from 64 to 196 (b) for n = 784, σ x = σ / n = 5.6/28 = .2, whereas for n = 49, σ x = 5.6/7 = .8 the standard error of the mean is increased from .2 to .8 when the sample size is decreased from 784 to 49 Sec. 8.5. (6) (a) μ x = μ = 174.5, σ x = σ / n = 6.9/5 = 1.38 (given n = 25) (b) z 1 = (172.45 – 174.5)/1.38 = -1.49; z 2 = (175.85 – 174.5)/1.38 = .98 where we add/subtract .05 due to the given precision of measurement of 0.1 cm. Hence P(172.5 < X < 175.9) = P(-1.49 < Z < .98) = .8365 - .0681 = .7684. And so the number of sample

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Homework Solutions 07 - (W4150 Intro to Probability and...

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