A task will be randomly assigned to one of three machines: To machine A with pro
ID: 3023115 • Letter: A
Question
A task will be randomly assigned to one of three machines:
To machine A with probability of 0.6
To machine B with probability of 0.3
To machine C with probability of 0.1
Machine A can complete the task in a random time with mean 10 hours and standard deviation 10 hours
Machine B can complete the task in a random time with mean 30 hours and standard deviation 20 hours
Machine C can complete the task in a random time with mean 50 hours and standard deviation 5 hours
If T is the total time to complete the task, calculate Var(T).
Explanation / Answer
A task will be randomly assigned to one of three machines:
To machine A with probability of 0.6
To machine B with probability of 0.3
To machine C with probability of 0.1
Machine A can complete the task in a random time with mean 10 hours and standard deviation 10 hours
Machine B can complete the task in a random time with mean 30 hours and standard deviation 20 hours
Machine C can complete the task in a random time with mean 50 hours and standard deviation 5 hours
If T is the total time to complete the task, calculate Var(T).
Var(T) =0.62 * var(A)+ 0.32 * var(B)+ 0.12 * var(C)
=0.62 * 100+ 0.32 * 400+ 0.12 * 25
=72.25
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