Question

Part 1

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 72 and standard deviation 3.

(b) If the acceptable range of hardness is (72 − c, 72 + c), for what value of c would 95% of all specimens have acceptable hardness? (Round your answer to two decimal places.)
(c) If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten? (Round your answer to two decimal places.)
_______  specimens
(d) What is the probability that at most eight of ten independently selected specimens have a hardness of less than 74.52? [Hint: Y = the number among the ten specimens with hardness less than 74.52 is a binomial variable; what is p?] (Round your answer to four decimal places.)

Part 2

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following.

F(x) = sum of {

0		x < 0
x2 25		0 ≤ x < 5
1		5 ≤ x

(f) Calculate E(X).
(g) Calculate V(X) and σ_x.

V(X)	=
σx	=

(h) If the borrower is charged an amount h(X) = X² when checkout duration is X, compute the expected charge

E[h(X)].

Answer 1

du