Engineering Assignments

a. Suppose that 30% of all students who have to buy a text for aparticular course want a new copy(the successes!), whereas theother 70% want a used copy. Consider randomly selecting 25 purchasers.

b. What is the probability that the number who want new copies ismore than two standard deviations away from the mean value?

c. The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text, what is theprobability that all 25 will get the type of book they want fromcurrent stock? {hint: Let X = the number who want a new copy. Forwhat values of X will all 15 get what they want?)

d. Suppose that new copies cost $100 and used copies cost $70.Assume the bookstore currently has 50 new copies and 50 usedcopies. What is the expected value of total revenue from the saleof the next 25 copies purchased? Be sure to indicate what rule ofexpected value you are using.

(hint : let h(x) = the revenue when X of the 25 purchasers want newcopies. Express this as a linear function)

A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations. a. If 15 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulations? b. If there are 500 firms in the area, of which 150 are in violation, approximate the pmf of part (a) by a simpler pmf. c. For X = number among the 10 visited that are in violation, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b).