Erroneous Answer Key? The problem I am working on is:

The current in a certain circuit as measured by an ammeter is a continuous random variable $X$ with the following density function: $f(x) = .075x + .2$ for $3 \le x \le 5$ and $0$ otherwise.
a. Graph the pdf and verify that the total area under the density curve is indeed 1.
b.Calculate $P(X \le 4)$. How does this probability compare to $P(x < 4)$?
c. Calculate $P(3.5 \le X \le 4.5)$ and also $P(4.5 < X)$.

For part a), I obviously got 1. However, the answer key says .25, how did they ever get that?
For part b), I found the answer to be .4625. The answer key says the answer is .50
For part c), I found the probability for the first one to be .5, and for the second one, .2781. The answer key says that the answer is simply .4375

You are right in a. and b., which made me not bother checking c. as you probably are right again. Considering that the answer key says a density integrates to $0.25$, you should probably be not too surprised, and assume - if you diverge - you are correct. 
