IE 111 Fall 2007
Homework #5
Due Wednesday October 10 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(0,100,.7,TRUE)
=BINOMDIST(0,100,.7,FALSE)
=BINOMDIST(100,100,.7,TRUE)
=
BINOMDIST(100,100,.7,FALSE)
The syntax is BINOMDIST(x,N,p,TRUE) for cumulative prob’s and
BINOMDIST(x,N,p,False) for PMF values.
Thus the answer is BINOMDIST(100,100,.7,FALSE)
(b) Which one of the following Excel formulas will calculate Pr(X>=65) ?
=BINOMDIST(65,100,.7,TRUE)
=1BINOMDIST(65,100,.7,TRUE)
=BINOMDIST(65,100,.7,FALSE)
=1BINOMDIST(65,100,.7,FALSE)
=BINOMDIST(64,100,.7,TRUE)
=
1BINOMDIST(64,100,.7,TRUE)
=BINOMDIST(64,100,.7,FALSE)
=1BINOMDIST(64,100,.7,FALSE)
Question 2
The faster we force our drilling 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 drill speed).
Suppose we want Pr(time until next breakdown > 30 days) =
90%.
What value of “p” will just satisfy this requirement?
P(X>30) = P(No breakdowns in first 30 days) = (1p)
30
Set (1p)
30
= 0.9 and solve:
(1p)= (0.9)
1/30
=
0.996494
so p= 0.003606
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 10 US Senators
out of the set of 100 Senators.
(b) The number of bad resistors in a roll of 1000 resistors.
(c) The result of a single die roll.
(d) The number of children that a couple has until they have a girl (ignore twins).
(e) The number of people that show up for an airline flight.
(f) The number of free throws I must shoot until I make a total of ten.
(g) A Negative Binomial (also called Pascal) distribution with r=1.
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View Full Document(a) Hypergeometric
(b) Binomial
(c) Discrete uniform
(d) Geometric
(e) Binomial
(f) Negative Binomial (or Pascal)
(g) Geometric
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?
N=
8
12
p=
0.45
0.35
P(2 or more good)
0.936819
0.957559
Uses formula of the form 1BINOMDIST(1,N,P,TRUE)
OR
Company A = 1
8
C
0
(0.45)
0
(10.45)
80

8
C
1
(0.45)
1
(10.45)
81
Company B = 1
12
C
0
(0.35)
0
(10.35)
120

12
C
1
(0.35)
1
(10.35)
121
Question 5
A study to evaluate a new medicine has been tracking a set of people for the last few
years.
As of last year’s survey, 50 people remained in the study.
It’s time for another
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 Spring '07
 Storer
 Probability, Binomial distribution, Negative binomial distribution, Geometric distribution

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