$$\begin{align} Z&\sim \mathcal N(0,1) \end{align}$$
$$ \text{Find the value of }~~ c ~~\text{such that}~~ P(Z<c)=0.65$$
$$ \Phi(x):=\int_{-\infty}^{x}f_{\text{s} }(x) \mathrm dz $$
Following values are known from the table of normal distribution.
$$ \Phi(0.38)=0.6480~~,~~\Phi(0.39)=0.6517 $$
What I can't understand currently is the following equation.
$$\begin{align} c&=0.38+{0.65-0.6480 \over 0.6517-0.6480 }(0.39-0.38)\\&=0.385 \end{align}$$
The book states that the interpolation was used here.
Can you tell me the logic which is used here, or some useful link for which describes of it?
BTW I independently got $0.385$ using a functional calculator with greedy way(this could be done since $~ \Phi(x) ~$ is an increasing function) but too stupid way it is.
ADD
$$\begin{align} a&:=0.38\\ b&:=0.39\\ \Phi_a&:=\Phi(a)\\ \Phi_b&:=\Phi(b)\\ \Phi'_b&:=\Phi_b-0.0017 \\ c&=a+ {\Phi'_b -\Phi_a\over \Phi_b-\Phi_a }(b-a) \end{align}$$