1. Let W = a drum tare weight in pounds (i.e., the weight of the empty drum). Suppose W "' N(58, 0.13).
(a) Find P(W > 58.5).
(b) Find P(57.8 W 58.2).
(c) Find the 99th percentile of W.
(d) Find the 10th percentile of W, and explain what it stands for.
2. Use the fact that an N ( µ, cr2 ) random variable Y can be written as Y = er Z +µ to show that Qy (p ) = crQz (p ) + µ.
3. By differentiating the distribution function of a WEIB( 8,,6) random variable (equation (4.3.28) ), show that its density is given by equation (4.3.29).