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Unformatted text preview: Mat 183 Fall 2002 Final Exam Name:
(Please print) Signature: Recitation: Em W‘ *" Instructions: Each problem is worth 5
points. Show all the work you want graded \\
on this exam. Unsupported answers may receive little or no credit. List the values If
and commands that you enter into your i
calculator. ® Part I  Probability 1. From a pool of 25 women and 18 men, a group of 12 people
is to be chosen for a medical study. ( a) How many different samples are possible ? ( b ) How many different samples contain an equal number of women and
men? 2. Let A and B be events with Pr(A) = 0.6 , Pr(B) = 0.7 and Pr(A U B) = 0.9.
Compute the following: (a) Pr(A m B) (b) Pr(A a B) (c) Pr(Am B ') (d) Pr(B I A‘ ) 3. A class has 10 students, 3 of whom are ﬁrst year students. An experiment consists of randomly
selecting students one at a time without replacement, until either three students have been chosen or
a ﬁrst year student has been chosen. (a) 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 ﬁrst year student on the second
selection? 4. An urn contains 6 red and 4 green balls. A sample of three balls is drawn all at once and the
number of red balls is noted. (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 5. A bottling company sells a product with a labeled volume of 16 ounces. The actual volume is
normally distributed with mean u = 16.15 oz. and standard deviation 0 = 0.05 02. (a) What is the probability that a randomly selected bottle actually contains at least 15.9 ounces?
Round your answer to 4 decimal places. (b) The manager of the company wants to know the volume so that there is a 0.8 probability that a
randomly selected bottle will contain more than this amount. What is the amount? Round your
answer to 2 decimal places. 6. John saves for 12 years. He deposits $200 into a savings account that earns 5.5% interest
compounded monthly at the end of each month for 5 years and then increases his monthly savings to $250 for the remaining 7 years. How much money will he have at the end of the 12 years? 7. Jane borrows $220,000 at 7% interest compounded monthly to start a new business. (a) If the loan is to be paid off in monthly payments for 25 years, how much will her payments be? (b) After 7 years of payments (from part (a)), she arranges to change her payments to $3500 per
month. How many more months will it take to pay off the loan? Round your answer to one
decimal place. Part III  Linear Algebra 8. (a) Pivot the following matrix about the circled element. l 3 2 4
3 9 6 0
2 ~5 5 7
,. , _ 3 a —1 2 c ~3
(b) 11) Fmd a, b,candd 1f  z . a=
—1 4 b 3 5 d
b:
C:
d:
9. Find all solutions to the system of equations in each case.
x+2y+4z=3 x—y+z=3
(a) 2x—3y+z=l3 (b) 2x+y+llz=4
x —3z=—5 x+y+7z=2 x+y—22=1
(c) —2x—3y+3z=—7
x—y—4z=*9 10. A business has a plastics division and a metal division. For each $1 worth of output the plastics
division needs $0.20 of output from the plastics division and $0.35 from the metal division. For
each $1 worth of output the metal division needs $0.15 of output from the plastics division and
$0.22 from the metal division. (a) Give the input—output matrix for this problem. (b) What level of production should each division have to meet a demand of $92,500 wonh of
plastics and $86,000 worth of metal? ...
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This note was uploaded on 06/17/2011 for the course MATH 183 taught by Professor Na during the Spring '09 term at University of North Carolina School of the Arts.
 Spring '09
 NA

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