Let X1, X2, ……., Xnbe a random sample from a continuous probability distribution having...

Let X₁, X₂, ……., X_nbe a random sample from a continuous probability distribution having median

a. Show that

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:

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 x_i’s and denote the second largest of the x_i’s. What is the confidence level of the interval