Review Questions to Prepare for the Exam
1)
George Constanza, the character on Seinfeld, is a perpetual loser who keeps
trying.
As long-time viewers of the show know, only 10% of the women George
approaches are willing to go out with him.
George often will introduce himself, and then
preface his invitation by saying “So waddya doin’ Friday night?”
Three quarters of the
women who don’t want to go out with him tell him they are busy –
“I’m giving my
Doberman a bath.”
Only one quarter of the women who are willing to go out with him
say they are busy.
If George finds a woman who admits to being free on Friday night,
what is the probability she will go out with him?
2)
A random sample is drawn from a population believed to be approximately
normally distributed.
The sample values are
6, 18, 3, 21, 16, 9, 13, 14, 17
a)
From this sample, compute the sample mean, sample median, sample standard
deviation.
b)
Compute a
98%
confidence interval for
µ
.
c)
If you wanted to verify the claim that the population is approximately
normally distributed, what graphical procedure could you use?
Explain what
would you be looking for.
<Hint: While a histogram or dotplot isn't a bad
idea, the right answer is a more sophisticated tool.>
3)
A student is rushing off to class when she remembers she needs to bring two floppy
disks with her.
She has 10 disks on her desk, but unfortunately four of them are
defective, and she doesn’t know which four.
Being in a hurry she grabs three disks at
random, figuring that there will probably be two good ones among the three.
a)
What is the probability that
at least two
of the three disks are good?
b)
She has three hours of work to do on the computers at the lab.
During the
day, network crashes occur randomly and independently at the rate of a crash
every 35 hours.
What is the probability she will experience exactly one
network crash while working in the computer lab?
4)
Suppose the GPA’s of prospective Commerce majors at Virginia are normally
distributed with a mean of 3.05 and a standard deviation of .31.
a)
What percentage of prospective Commerce majors have at least a B (that is,
3.0) GPA
b)
If the Commerce department wanted to pick a minimum GPA to use as a
cutoff for admission to their program, and wanted a rule that would eliminate the
weakest 35% of its applicants, what minimum GPA would it select?