Statistical Analysis of Work-Hours Distribution and Probability Calculations

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Statistical Analysis of Work - Hours Distribution and Probability Calculations Overall, the amount of work - hours involved in the festival preparation by company employees is normally distributed around 150 hours with a standard deviation of 20 hours. 1) How likely (what is the probability) is it that somebody will have his involved work - hours between 140 and 170? Solution. Let X be the amount of work - hours involved in the festival preparation by company employees . Then we know that X follows a normal distribution with . 20 , 150 = =   So, the probability that somebody will have his involved work - hours between 140 and 170 is ) 170 140 (   X P Note that ) 1 , 0 ( ~ 20 150 N Z X − = . So, ) 170 140 (   X P ) 5 . 0 ( ) 1 ( ) 1 5 . 0 ( ) ( 20 150 170 20 150 20 150 140 −  −  =   − =   = − − − Z P Z P Z P P X By looking up the z - table, we have 3085 . 0 ) 5 . 0 ( 8413 . 0 ) 1 ( = −  =  Z P Z P So, ) 170 140 (   X P 5328 . 0 3085 . 0 8413 . 0 ) 5 . 0 ( ) 1 ( = − = −  −  = Z P Z P
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