Suppose an investigator wants a confidence interval for the median of a continuous distribution based on a random sample _{1},…, _{n} without assuming anything about the shape of the distribution.

a. What is P(_{1} ), the probability that the first observation is smaller than the median?

b. What is the probability that both the first and the second observations are smaller than the median?

c. Let _{n} 5 max {_{1},…, _{n}}. What is P(y_{n} )?

d. With _{1} min {x1,…, xn}, what is P( _{1})?

e. Using the results of parts (c) and (d), what is P(_{1} _{n})? Regarding (y_{1}, y_{n}) as a confidence interval for , what is the associated confidence level?

f. An experiment carried out to study the curing time (hr) for a particular experimental adhesive yielded the following observations:

Referring back to part (e), determine the confidence interval and the associated confidence level.

g. Assuming that the data in part (f) was selected from a normal distribution (is this assumption justified?), calculate a confidence interval for (which for a normal distribution is identical to ) using the same confidence level as in part (f), and compare the two intervals.