How to generate a random variable (exponential) with a specified mean

Question

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i have been asked to generate a set of random numbers. the sum of the 5 exponentially distributed numbers should be 8, 9, 10, 11, and 12 hrs. how can you do that?

Original problem below:

A manager is interested in a determining whether a system passes a performance specification. For purposes of this problem, the technical performance metric (TPM) is calculated by summing 5 Exponentially distributed random variables with an averages of 8, 9, 10, 11, and 12 hrs. Write a script to simulate 10 replications of the TPM and calculate the 95% confidence interval. The specification indicates the TPM should be less than 50 hrs. Does the system pass the performance test with the requisite confidence interval?