8.11 A random variable has the following density function.

f(x) = 1 - .5x 0 < x < 2

1. Graph the density function.
2. Verify that f(x) is a density function.
3. Find P(X > 1).
4. Find P(X < .5).
5. Find P(X = 1.5).

10.23 How many rounds of golf do physicians (who play golf) play per year? A survey of 12 physicians revealed the following numbers:

3 41 17 1 33 37 18 15 17 12 29 51

Estimate with 95% confidence the mean number of rounds per year played by physicians, assuming that the number of rounds is normally distributed with a standard deviation of 12.