78. The previous two exercises considered a CI for a population median based on the n order statistics from a random sample. Let s now consider a prediction interval for the next observation Xn1.

a. What is P(Xn1  X1)? What is P({Xn1  X1}

{Xn1  X2})?

b. What is P(Xn1  Y1)? What is P(Xn1 Yn)?

c. What is P(Y1  Xn1  Yn)? What does this say about the prediction level for the PI (y1, yn)? Determine the prediction level and interval for the data given in the previous exercise.