(20 pts) Let X be a Gamma random variable with unknown mean and unknown vari ance. Through simulation? we built a 95% condence interval for the expected value of X and this interval came out to be [24,30]. Assume that we used 100 replications to build this condence interval. Find an interval [I]? U] such that X is contained in [L, U] with probability approximately 0.95. (HINTS: A Gamma distribution with shape 0: and rate ,3 ( f(.'17) : litigate155$) has mean cz/ and variance 05/52. The function GAMMA.INV(p,0,B) in Excel returns value U such thatl P(X S U ) = p where X is a Gamma random variable with parameters a and ,6')