D Period and F Period Statistics
Worksheet for Students not on NSA Field Trip
This will be graded. Submit paper in Room R at end of F period 5/17/00.
If you have an excused absence for 5/17, due date is 5/18.

Assume that the heights of American men are normally distributed with mean 70 inches and standard deviation 3 inches, and that the heights of American woman are normally distributed with mean 65 inches and standard deviation 2.5 inches. Let the random variable X denote the height of a randomly selected man, Y the height of a randomly selected woman, and Y – X the difference in heights between an independently selected woman and man.

(a) What does P(Y > X) mean in plain English?
(b) Showing sufficient (though not excruciating) detail, use a simulation procedure to estimate an answer to part (a). Include a marked-up random digit table or a listing of any calculator-based procedure you use.
(c) Use the formulas involving means and variances of random variables to compute an answer to part (a) correct to 4 decimal places. Hint: You can also think of the probability as P(Y – X > 0).
(d) What assumptions did you use in part (c)?

Collaboration with other students, including calculus students, is permitted if you document it. However, copying is not allowed. Each student must submit an original writeup.