Introduction to Operation Engineering Management Decision Analysis You can solve

Introduction to Operation Engineering Management Decision Analysis
You can solve this problem as a team, however, each student should submit his/her solution separately.
Work Load Estimation (Central Limit Theorem):
Your company is involved in 30 projects.
Inspecting and reviewing the progress of each project takes between 20 to 30 minutes.
1. On average how long will it take to review all the projects?
2. Let Xi be a uniformly distributed random variable between 20 and 30. One way to generate such a random variable in EXCEL is 20 + 10*RAND(). Sum of 30 of such random variables ∑Xi is one realization of such an inspection. Repeat this realization 400 time.
a) Determine the number of times that the total time of inspection takes more than 13 hours. Dividing this number by 400 give the chance that the inspection will take more than 13 hours
b) Determine the number of times that the total time of inspection takes less than 12 hours. Dividing this number by 400 give the chance that the inspection will take less than 12 hours
c) Extra Points:
Can you use the Central limit theorem to estimate the probabilities in a) & b)?