In: Math
A repairman has 20 jobs that need to be completed today. Usually, 70% of all jobs are fairly straightforward, so that the time it takes to complete them is well-described by normal distribution with average 10 minutes and standard deviation 1 minute. The rest are challenging jobs, so that completion time is well-modeled with exponential distribution with average 1 hour.
i. If she starts at 8am, what is the expected time when she will finish all already assigned jobs?
ii. When asked when she will finish the jobs, she wants to give a safe answer by overestimating it by one standard deviation. Find the standard deviation for the time needed to finish all jobs.