3) Suppose that a 100-point test (scores are whole numbers) is administered to every high school student in the
USA at the start of their senior year and that the scores on this test are normally distributed with a mean of 70
and standard deviation of 10. If 5 scores are selected at random, what is the probability that exactly 3 of these
scores are between 65 and 75, inclusive?
4) Let X be a normal random variable with mean μ and standard deviation σ. Show that the expected value and
variance of the quantity x-μ/σ (this is x-μ over σ) are 0 and 1, respectively.