Consider the situation described in the previous exercise.

a.

b. What is the probability that exactly one of the n original observations is smaller than the median?

c.

d.

e. Determine the confidence level and CI using part (d) with the data given in the previous exercise.

Data From previous Exercise

In this exercise, we develop a CI for µ̃ that is valid whatever the shape of the population distribution as long as it is continuous. Let X₁, …, X_n be a random sample from the distribution and Y₁<..........<Y_n denote the corresponding ordered values (smallest observation, second smallest, and so on).

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What is P({X₁ <μ}{X₂ > µ}~\ n{Xn > μ}), that is, the probability that only the first observation is smaller than the median?