MAT183-2002Fall - Mat 183 Fall 2002 Final Exam Name:...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

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? ...
View Full Document

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.

Page1 / 6

MAT183-2002Fall - Mat 183 Fall 2002 Final Exam Name:...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online