IE 111 Spring 2009
Homework #5
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)
=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 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) = (1-p)
30
Set (1-p)
30
= 0.9 and solve:
(1-p)= (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.