APPLIED ENGINEERING STATISTICSISE 3293/5013Assignment 3Due Wednesday, September 10, 2014

Remember to show your work for calculation problems. You can use Excel or a calculator to calculate factorials, permutations, and combinations.

Problem 1Suppose that 70% of an inventory of the memory chips used by a computer manufacturer comes from Vendor 1 and 30% from Vendor 2. It is determined that 99% of the chips from Vendor 1 and 88% of the chips from Vendor 2 are not defective. (adapted from [Modarres et al. 2010])a. If a chip from the computer manufacturers inventory is selected and is defective, what is the probability that the chip was made by Vendor 1?b. What is the probability of selecting a defective chip (irrespective of the vendor)?

Problem 2A passenger air bag (PAB) disable switch is used to deactivate the PAB in cases when the passenger seat of a commercial van is not occupied. This saves the PAB from being wasted when the van gets into a frontal collision. The switch itself is an expensive component, so its feasibility needs to be justified based on the probability of the passenger seat being occupied when a collision happens. Available data show that a commercial van driver has a passenger 30% of the time. In addition, expert opinion analysis indicates that the driver is 40% less likely to get into a collision with a passenger than without one. Given that a frontal collision has occurred, what is the probability of the passenger seat in the commercial van was occupied? (adapted from [Modarres et al. 2010])

Problem 3There are 15 teams in the National Basketball Association (NBA) Western Conference. The conference is divided into 3 divisions, and each division has 5 teams. Assume that no two teams have identical records.a. How many different rankings of all 15 teams are possible?b. If each division is ranked separately, how many different rankings are possible?c. The Oklahoma City Thunder is one of the teams in the Western Conference. If each division is ranked separately, how many different rankings are possible where Oklahoma City is in first place in its division?

Problem 4A production facility employs 20 workers on the day shift, 15 works on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select six of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of six workers has the same chance of being selected as does any other group (that is, drawing six slips without replacement from among the 45). (adapted from [Devore 2009])a. How many selections result in all six workers coming from the day shift? What is the probability that all six selected workers will be from the day shift?b. What is the probability that all six selected workers will be from the same shift?c. What is the probability that at least two different shifts will be represented among the selected workers?d. What is the probability that at least one of the shifts will be unrepresented in the sample of workers?

Problem 5From a collection of five women and seven men. (adapted from [Ross 1998])a. How many different committees consisting of two women and three men can be formed?b. What if two of the men are feuding and refuse to serve on the committee together?

Problem 6Chapter 3, Exercise 3.90 in [Mendenhall and Sincich 2007].

Problem 7Suppose you have a standard 52-card deck of playing cards. Lets develop the likelihood that we are dealt a three of a kind. (adapted from [Sullivan 2007])a. How many ways can five cards be selected from a 52-card deck?b. Each deck contains 4 twos, 4 threes, and so on. How many ways can three of the same card be selected from the deck?c. The remaining two cards must be different from the three chosen and different from each other. For example, if we drew three kings, the fourth card cannot be a king. Further, if we drew three kings, the fourth and fifth cards cannot be the same (or wed have a full house). After selecting the three of a kind, there are 12 different ranks of card remaining in the deck that can be chosen. Of the 12 ranks remaining, we choose two of them and then select one of the four cards in each of the two chosen ranks. How many ways can we select the remaining two cards?d. Compute the probability of obtaining three of a kind when dealt five cards.

Problem 8 Show the following (use the variables dont simply plug in numerical values).