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?