If $\displaystyle S^2$ is the variance of a random sample which is drawn from a normal distribution $\displaystyle N(\mu,\sigma^2)$ then $\displaystyle cS^2$ has a standard distribution for a particular value of the constant c.

Specify the constant c. What is the distribution?

How many pairs of positive constants a; b exist such that $\displaystyle P(a < cS^2 < b) = 0.95$?