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Fundamentals of Statistics Section 95 Project #2 Instructor: Pete Wildman Spring Semester 2000 |
This project is due on Friday
March 3 - Have fun
1.
Approximately
10% of the general population is left handed
a.
If
nine people are randomly selected, find the probability that exactly two of tem
are left handed
b.
If 12
people are randomly selected find the probability that at least two of them are
left handed
c.
If 22
people are randomly selected find the probability that exactly three of them
are left handed
d.
Create
a probability distribution for the random variable x , where x represents the
number of left handed people in a randomly selected sample of 8 people. Find
the mean and standard deviation of this distribution
2.
On the
new International Space Station, The US lab is operated by a series of
computers. Each computer identical backups for safety (this is a result of the
Challenger accident and the fact that it is hard to get repairs into outer
space). These computers activate the internal thermal cooling system of the
lab, which will allow for human habitation in the lab. Your question is how
many backup computers will you need. A realistic probability one of these
computers will fail is 0.008. Use this probability and the binomial probability
formula to find the probability of 0, 1, 2, and 3 computer failures for the
internal thermal cooling system computer and 2 backup computers and the
probabilities of 0,1, and 2 computer failures for the internal thermal cooling
system computer and 1 backup computer. Summarize your results in table form.
Use the results from the tables and assume that the internal thermal cooling
system will work if at least one computer is working. Find the probability of
the system working with one backup and find the probability of the system
working with two backups. Write me a report summarizing your findings,
supporting them with specific results. Pretend that I am your supervisor at
NASA.
3.
The
purpose of this problem is to have you calculate the expected value for some
sweepstakes on the web. You can search (using your favorite search engine)
under the words sweepstakes rules and find your own sweepstakes. Your
sweepstakes should have at least 3 different levels of prizes and you will need
the dollar amount of each prize. You will also need an estimate of how many
will enter - this you will have to determine yourself. Overall here is what you
should submit to me:
a.
The
name of the contest, how you can enter and what you can win with dollar amounts
for the prizes
b.
An
estimate of how many will enter the contest and the probability for winning the
different prizes. You might include many different estimates
c.
A
calculation of the expected value for winning the contest. If you use different
estimates in part b - you should have many answers in part c
d.
A
discussion about whether you should enter the contest. Consider that even if
the contest costs nothing to enter - you will be giving them information about
yourself on the internet and at the very least this will probably result in
lots of junk mail in your mailbox
Try
to search for an interesting web site first - If you have no luck contact me
and I'll give you some
places to get started
GOOD LUCK AND HAVE FUN!