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Advanced Math/Quantitative Analysis for Managerial Applications

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Expert: - 8/11/2009


Question
1.Write a detailed note on Normal Distribution, Standard Normal Variety and the Central Limit Theorem. Illustrate the concepts with the help of diagrams.

2.   From the following data compute quartile deviation and the coefficient of skewness:

Size    4.5-7.5   7.5-10.5   10.5-13.5   13.5-16.5 16.5-19.5
Frequency   14   24   38   20   4

3.   A bank has a test designed to establish the credit rating of a loan application. If the persons, who default (D), 90% fail the test (F). Of the persons, who will repa the bank (ND), 5 % fail the test. Furthermore, it is given that 4% of the population is not worthy of credit (i.e. defaulters). Given that someone failed the test, what is the probability that he actually will default (When given the loan)?  

Answer
1. Here is the normal distribution: http://www.netmba.com/statistics/distribution/normal/

I only found for websites on Satandard Normal Variety.

http://www.springerlink.com/index/e220327kl2702362.pdf
This was the outline of a book on the subject.

http://www.slideshare.net/vksaini11/statistical-quality-control-presentation
This one had a list of references on the subject and who to contact in the text that started over two pages down in the document.

http://interstat.statjournals.net/YEAR/2008/articles/0802003.pdf: this required a more advanced version of adobe than I have.

http://www.ignou.ac.in/assignments/management/july_09/ms-8.doc
This was the subject matter on a class that is about the subject and related fields.
In the heading, it has "Quantitative Analysis for Managerial Applications."


2. The best way to do this would be to construct a histogram that was in the regions given.
I would draw vertical lines at 4.5, 7.5, 10.5, 13.5, 16.5, and 19.5.
In between each of the vertical lines, draw a horizontal line at the amount given.
That is, 14 for the 1st, 24 for the 2nd, 38 for the 3rd, 20 for the 4th, and 4 for the 5th.

3. We are told that 4% of the people will fail, which means that 96% of the people will pay back the loan.  Of the 4% who will not pay back the loan, the test will be failed 90% of the time, so that means 3.6% will fail that are truly bad.  Since 96% are OK, there are 5% that fail the test.  This means that there are 4.8% of the good people that will fail.

That means there is a total of 3.6% bad people that fail plus 4.8% of the good people,
for a total of 8.4%.  In other words, of those who fail, 3/7 are truly bad, but 4/7 are good.

This says that if the person has failed the test,
there is only a 3/7 chance they will truly fail on the loan
out of all of those that failed.

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