A random variable X is normally distributed with $\mu =60$ and $\sigma $ = 3. What is the value of 2 numbers a,b so that $P(X=a)=P(X=b)$.

The solution is $a=60$ and $b=65$.

However, I do not know how to come up with that answer. As far as I understand $P(X=a)$ and $P(X=b)$ have to be both 0 since you always have to give a range e.g. $P(a<X)$. Moreover if I insert the values 60 and 65 in the formula $Z=(X-\mu )/\sigma $ than I would end up with 0,1.667 and z-scores 0.5, 0.952 respectively.

The solution is $a=60$ and $b=65$.

However, I do not know how to come up with that answer. As far as I understand $P(X=a)$ and $P(X=b)$ have to be both 0 since you always have to give a range e.g. $P(a<X)$. Moreover if I insert the values 60 and 65 in the formula $Z=(X-\mu )/\sigma $ than I would end up with 0,1.667 and z-scores 0.5, 0.952 respectively.