# HW5_11 - IE 111 Fall 2011 Homework #5 Due Wednesday October...

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IE 111 Fall 2011 Homework #5 Due Wednesday October 12 in class Question 1 Let X be a Binomial random variable with n=100, p=.7 (a) Which one of the following Excel formulas will calculate Pr(X 100) ? =BINOMDIST(100,10,.7,TRUE) =BINOMDIST(100,10,.7,FALSE) =BINOMDIST(10,100,.7,TRUE) =BINOMDIST(10,100,.7,FALSE) (b) Which one of the following Excel formulas will calculate Pr(X 65) ? =BINOMDIST(65,100,.7,TRUE) =1-BINOMDIST(65,100,.7,TRUE) =BINOMDIST(65,100,.7,FALSE) =1-BINOMDIST(65,100,.7,FALSE) =BINOMDIST(64,100,.7,TRUE) =1-BINOMDIST(64,100,.7,TRUE) =BINOMDIST(64,100,.7,FALSE) =1-BINOMDIST(64,100,.7,FALSE) Question 2 The faster we force our milling machine to go, the more likely it is to break. Let's suppose that each day is an independent trial, and we can set the probability of the machine breaking to any value “p” that we choose (by controlling the speed). Suppose we want Pr(time until next breakdown > 20 days) = 95%. What value of “p” will just satisfy this requirement? Question 3 For each description, write the name of the appropriate distribution. Some distributions may be used more than once; others might not be used at all. (a) The number of Democrats, if we randomly select a committee of 5 US Senators out of the set of 100 Senators. (b) The number of broken eggs in a box of 12 eggs. (c) The result of a single die roll. (d) The number of children that a couple has until they have their second girl (ignore twins). (e) The number of ticket holders that show up for an airline flight. (f) The number of free throws I must shoot until I make a total of ten. (g) The number of shots I take in a basketball game until I make my first basket. Question 4 Clarinet reeds from Company A come in boxes of 8, and (historically) 45% of their reeds are good, on average. Clarinet reeds from Company B come in boxes of 12, and historically they have 35% good reeds. The two companies charge the same amount per box. We can assume all reeds are independent. If you were playing a single concert (for which you need two good reeds) and could only bring one box of reeds, which company gives you a better chance of having at least two good reeds?

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## This note was uploaded on 10/13/2011 for the course IE 111 taught by Professor Storer during the Fall '07 term at Lehigh University .

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HW5_11 - IE 111 Fall 2011 Homework #5 Due Wednesday October...

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