The amount of time needed for a certain machine to process a

The amount of time needed for a certain machine to process a job is a random variable with meanEXi=10 minutes and Var(Xi)=2 minutes2. The times needed for different jobs are independent from each other. Find the probability that the machine processes less than or equal to 40 jobs in 7 hours.

Solution

For Xi
Mean ( u ) =10
Standard Deviation ( sd )=1.414
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

Y =X1 + X2 + X3+....X40
EY = 40*10 = 400
Var(Y) = 40*2 = 80
P( less than 40 jobs in 7 hours) = P( Y > 7*60) =    P( Y > 420)
P(X > 420) = (420-400)/8.944
= 20/8.944 = 2.2361
= P ( Z >2.236) From Standard Normal Table
= 0.0127