Suppose that there are 1000 students in Stanford housing, and one night each student independently has a 1% chance of ordering pizza. Let X be the number of students who order pizza.

a) Approximate X by a Poisson random variable. (That is, X Poisson() for what value of ?).

Similarly, approximate X by a normal random variable. (That is, find and ²)

b) Estimate the probability that at most two students order pizza, using both your Poisson approximation and your normal approximation. Which approximation do you trust more? (You can give a qualitative reasoning.)