Let X1, X2,..., Xn be a random sample from a continuous probability distribution having median m, (so that P(Xi ¤ µÌ) = P(Xi ¥ µÌ)

Let X1, X2,..., Xn be a random sample from a continuous probability distribution having median m, (so that P(Xi ‰¤ µÌƒ) = P(Xi ‰¥ µÌƒ) = .5).
a. Show that

So that (min(xi), max(xi)) is a 100(1 - α)% confidence interval for µÌƒ, with α = (1/2)n-1.
b. For each of six normal male infants, the amount of the amino acid alanine (mg/100 mL) was determined while the infants were on an isoleucine-free diet, resulting in the following data:
2.84 3.54 2.80 1.44 2.94 2.70
Compute a 97% CI for the true median amount of alanine for infants on such a diet ("The Essential
Amino Acid Requirements of Infants," Amer. J. of Nutrition, 1964: 322-330).
c. Let x(2) denote the second smallest of the xi's and x(n-1) denote the second largest of the xi's. What is the confidence level of the interval (x(2), x(n-1)) for µÌƒ?

Pimin (K) < < max (Xi),-1-( 2