It is possible to construct a nonparametric tolerance interval that is based on the extreme values in a random sample of size n from any continuous population. If p is the minimum proportion of the population contained between the smallest and largest sample observations with confidence 1 €“ a, it can be shown that and n is approximately

(a) In order to be 95% confident that at least 90% of the population will be included between the extreme values of the sample, what sample size will be required?
(b) A random sample of 10 transistors gave the following measurements on saturation current (in milliamps): 10.25, 10.41, 10.30, 10.26, 10.19, 10.37, 10.29, 10.34, 10.23, 10.38. Find the limits that contain a proportion p of the saturation current measurements at 95% confidence. What is the proportion p contained by these limits?

np" - - (n - 1)p" = a +p\(xa4 - p) Xa,