A forward-thinking owner of automobile dealerships has decided to open three Tesla
dealerships: one in Washington D.C., one in Baltimore, and one in Philadelphia. The monthly
demand for cars at all three dealerships is estimated to be identical and follow a normal
distribution with mean μ = 36, and standard deviation σ = 12. Each dealership begins the month
with an inventory of 50 cars, and gets no additional shipment until the following month.
a. For a specific dealership, what is the probability that it runs out of cars by the end of
the month?
b. What is the probability that at least one of the three dealerships runs out of cars by the
end of the month?
c. What is the probability that the total demand of the three dealerships exceeds 120
cars in a month?