It is possible to construct a nonparametric tol- erance 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 con- tained between the smallest and largest sample observa- tions with confidence 1-a, it can be shown that and is approximately - (n-1)*-a ()()+

(a) In order to be 95% confident that at least 90% of the population will be included between the extreme val- ues of the sample, what sample size will be required?

(b) A random sample of 10 transistors gave the follow- ing measurements on saturation current (in mil- lamps): 10.25, 10.41, 10.30, 10.26, 10.19, 10.37, 10.29, 10.34, 10.23, 10.38.

Find the limits that con- tain a proportion p of the saturation current meas urements at 95% confidence. What is the proportion p contained by these limits?