Two fair dice are rolled. Let X be the absolute difference between the outcomes of
the dice. For example, if the outcomes are 2 and 6, then X = 4 .
(一) Find the p.m.f. and c.d.f. of X . (5%)
(二) Find P(0 < X ≤ 3) and P(1≤ X < 3) . (5%)
Brakes Shop, Inc., is a franchise that specializes in repairing brake systems of
automobiles. The company purchases brake shoes from a national supplier. Currently,
lots of 1,000 brake shoes are purchased, and each shoe is inspected before being
installed on an automobile. The company has decided instead of 100% inspection to
adopt an acceptance sampling plan.
(一) Explain what is meant by the acceptance sampling plan, and state its null
hypothesis. (4%)
(二) The manager of the quality control department of the company is willing to tolerate
both 0.10 probability of rejecting a lot with 20 defective items and 0.20 probability
of accepting a lot with 150 defective items. Give an acceptance sampling plan that
can meet the requirements, and justify your answer. (8%)
The marketing department of a company has designed three different boxes for its
product. It wants to determine which box will produce the larges amount of sales. Each
box will be test marketed in five different stores for a period of a month. Below you are
given the information on sales.
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