Erroneous Answer Key?

Question

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

Answer 1

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.