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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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) ]
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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