A factory employing a large number of workers finds that over a period of time , the average absentees rate is three workers per shift. Calculate the probability that in a given shift (i)exactly two workers will be absent , (ii)more than four workers will be absent .

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2014-08-24T10:49:40+05:30

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Assume that the probability distribution function is a normal distribution function, with the parameter x = number of employees absent in a shift.

Average = expected value of x  = E(x) = Mu = 3

Function Ф[(x-3)/sigma] = kumulative probability function for normal distribution function.

1 )  probability that exactly 2 empoyees are absent:      Ф(2) - Ф(1)

               = 1/2  [ erf (2/√2) - erf(1/√2) ]

2)  probability that more than 4 are absent :  (x - Mu) / sigma  > 1
                  
                   = 1/2  [ 1 - erf(1/√2) ]

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