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Assignment _1 solutions

# Assignment _1 solutions - Homework Assignment#1 Solutions...

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Homework Assignment #1 Solutions DSCI 305 1.86 (a) From Table A, P(z < 2.85) = .9978; or using an Excel function, NORMSDIST(2.85) (b) P(z > 2.85) = 1 - P(z < 2.85) = 1 - .9978 = .0022; or using an Excel function, 1 – NORMSDIST(2.85) (c) P(z > - 1.66) = 1 - P(z < - 1.66) = 1 - .0485 = .9515; or using an Excel function, 1 - NORMSDIST( - 1.66) (d) P( - 1.66 < z < 2.85) = P(z < 2.85) – P(z < - 1.66) = .9978 - .0485 = .9493; or using an Excel function, NORMSDIST(2.85) – NORMSDIST( - 1.66) 1.88 (a) The z-score for the proportion of .25 is - .675 (average of - .67 and - .68); or using an Excel function, NORMSINV(.25) (b) The z-score for the proportion of 1 - .40 or .60 is .255 (average of .25 and .26); or using an Excel function, NORMSINV(1 - .40) 1.104 (a) 2 266 2 16 234 μ σ - = - × = and 2 266 2 16 298 μ σ + = + × = . Between 234 and 298 days. (b) 234 days or less (c) It is unlikely since 218 is three standard deviations below the mean. Only 0.15% of all women give birth in 218 days or less. 1.110 Let x be the length of human pregnancies from conception to birth. x ~ N(266, 16) (a) 0516 . ) 63 . 1 ( 16 266 240 ) 240 ( = - < = - < - = < z P x P x P σ μ or 5.16%. (b) . 5987 . ) 25 . 0 ( 16 266 270 ) 270 ( = < = - < - = < z P x P x P σ μ 5471 . 0516 . 5987 . ) 240 ( ) 270 ( ) 270 240 ( = - = < - < = < < x P x P x P or 54.71% (c) The z-score for the proportion of .80 is .84.

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Assignment _1 solutions - Homework Assignment#1 Solutions...

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