You own a coffee shop and sell a light and a dark roast. Assume your customers order coffee independently of one another, and the probability of a customer ordering a dark roast coffee is 0.4. Let X be the random number of customers ordering a dark roast coffee of a typical morning rush hour customer count of 75. Compute the following:
A. P(X<=35)
B. P(X>=45)
C. If you are low on dark roast and only brewed enough dark roast to handle 55 customers during the morning rush hour, what's the probability you'll run out of dark roast?
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