1. The problem statement, all variables and given/known data Generalize: For arbitrary 0 < p < 1, show that the method giving a and b produces the minimum length interval. Hint: It might be helpful to use local extrema for the inverse function of the distribution function. 2. Relevant equations The method is is talking about is locating the z scores using (1-p)/2 and [1-(1-p)/2] 3. The attempt at a solution Let a be the area on the tail end of the distribution not included in p Let b be the other end so that a+b=1-p and b=1-p-a Then the points A and B are the end points of the interval containing p. B-A = (F^-1)(p+a)-(F^-1)(a) This is where I am stuck. I know f(y). So d/dy(F(y))=f(y) and then (f^-1)'(y)=1/(f'(f^-1)(y)) I am not sure how to proceed.