Q.Suppose error involved in making a certain measurement is continuous r.v. X with p.d.f. f

As in Exercise 7.2 Q7, $k=3/32$, so $f(x)=\dfrac3{32}(4-x^2)$.

1. By symmetry, $P(X>0)=1/2$.
2. $P(-1<x<1)=\dfrac{11}{16}$.
3. As printed, this condition is 'X < 0.5 OR X > 0.5', i.e. every real number except exactly X=0.5. For a continuous random variable a single point always has probability 0, so $P(X=0.5)=0$ and $P(X<0.5\text{ or }X>0.5)=1-0=1$. (This differs from Exercise 7.2 Q7(iii), printed with a minus sign as '−0.5 < x or x > …

Recognise that 'X<c or X>c' covers every real number except the single point X=c, whose …

Assuming this must give the same numeric answer as the similarly-worded Exercise 7.2 Q7(iii); the two printed conditions differ …