Question

Consider computer jobs that run a cluster. The running time (in minutes) of each job follows...

Consider computer jobs that run a cluster. The running time (in minutes) of each job follows a normal distribution with mean 15 and variance 4. How many jobs can someone submit to the cluster at most so that with a probability of at least 0.95 he/she is certain that the total running time of the computer jobs will not exceed 200 minutes?

Math   Statistics-And-Probability   
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Answer #1

We are given

Also:

We need to find n such that:

Comparing we get:

Solving

Hence n should be 12 for the total running time not to exceed 200.

Hence 12 jobs can be submitted to the cluster at most so that with a probability of at least 0.95 he/she is certain that the total running time of the computer jobs will not exceed 200 minutes

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

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