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Unformatted text preview: Mat 183 Spring 2002 Final Exam Name:
( please print) Recitation Time:
Recitation Instructor : Obterrieder Buzaianu Instructions: Show all the work you want
graded on this exam. Unsupported answers
may receive little or no credit. List the values
put into your calculator and the speciﬁc
program being used. Part I — Probability l. ( a) How many 5 letter words ( including nonsense words ) can be made {mm the letters L, A , T , S , K , E , and M if words must end with a vowel and
letters cannot be repeated ? (b) E andFareevents with Pr(E)=0.3,Pr(F)=O.5andPr(E UF)=0.7.
Are E and F independent ? 2. A class has 10 students , 4 of whom are seniors . An experiment consists of Randomly selecting students one at a time without replacement, until either
three students have been chosen or a senior is chosen. ( 3) Draw a tree diagram to illustrate this experiment. Include probabilities
along the branches. ' ( b ) What is the probability that the experiment ends by getting a senior on
the second selection ? 3. An urn contains 6 red and 4 green balls. Three balls are drawn without
replacement and the number of red balls is observed. ( a ) Make a probability distribution table for the number of red balls drawn. (b ) What is the expected value for the number of red balls drawn ? Part II — Statistics and Math of Finance 4. The weight of bowling balls produced by a factory is normally diStributed with a
mean of 15.1 pounds andastandard deviation of .7 pounds. Let X be a random variable whose possible values are the weights of the balls produced by
the factory . (a) Find Pr( 12.2 5X5 17.3) ( b) Find the weight which separates the bottom 6 % of the balls from the rest. 5. (a) If for 25 years you deposit $ 100 at the end of each month into an account
paying 5.4 % annually , what will your ﬁnal balance be ? ( b) Suppose you borrow $ 180,000 at 7 % interest compounded monthly
to start a new business. Assume the loan is to be paid off in 15 years. ( l ) What are your monthly payments ? ( 2 ) What is the balance on your loan after 9 years ? 6. Consider the difference equation y” =1 y,,_, +4, yo = 5. (a) Findtheline y=—]—b—.
—a ( b) ls its graph constant, monotone , or oscillating ? Why ? ( c) Is its graph attracted to or repelled by the line ? (d) Make a table displaying the values y0 through )15 . ( Use TI83 ) Part III  Linear Algebra 7. Using the rref command ﬁnd all solutions to the following system of equations. x+2y—z=3
x—y+z=4
2x+4y~22=6 8. Pivot the following matrix about the indicated only. 3—125
1462
(2)1—19 9. The economy of Narnia consists of two industries, oil and steel. The oil industry
consumes $ .06 of oil and S .10 of steel to produce 3 l of oil. The steel
industry consumes S .29 of oil and $ .15 of steel to produce 3 l of steel. ( a) What is the Input—Output matrix for this economy ? (b ) At what level should each industry produce in order to have $ 18 million
of oil and $ 23 million of steel available for export ? ...
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