Let Yi <>Y2 <>···<>Y48 be the order statistics of a random sample of size 48 from a distribution of the continuous type. We want to use the observed interval (y4 , y45 ) as a lOOy percent tolerance interval for 75 percent of the distribution.

(a) To what is y equal?

(b) Approximate the integral in part (a) by noting that it can be written as a partial sum of a binomial p.d.f., which in turn can be approximated by probabilities associated with a normal distribution.