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 meanEX_i=10 minutes and Var(X_i)=2 minutes^2. 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.

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Solution

Mean = np = 10

variance =npq =2

Thus q = 0.2 and p = 0.8

n = 12.5 or 13

P(machine prcesses <=40 in 7 hours)

= P(machines takes more than 40/7 for one job)

x = 5.714

mu = 10

Z = 5.714-10/2/rt 7 = -5.669

P(Z>-5.669) = 1.00(almost certain)