Suppose that in the car show Top Gear, "the Stig" is trapped in a snowy mountain in Canada, left with food supply for only 5 days. The rescue team, currently in Vancouver, has decided to split into two groups and drive cars with 2 different strategies.

Team A will drive a Mustang from Vancouver to town C near snowy mountain (with estimated time Uniform(3, 4) in days) and then switch to an F150 Raptor to climb the mountain (with estimated time Uniform(1, 1.5) in days).

Team B will drive a Range Rover for the whole trip (with estimated time Uniform(4, 6) in days).

A. (10) Develop a mathematical model using random variables and describe how it can be used to capture the probability that "the Stig" will be rescued in time. Define the inputs, the outputs, and define the quantities of interest needed to answer the question.

B. (15) Describe how you would use spreadsheets to conduct a Monte Carlo Simulation to figure out the above probability. Provide the detailed Excel formulas for a single run. Describe how you would simulate 100 runs and use what data as sample and how to derive a 95% confidence interval.