MATHEMATICS DISCIPLINE
UNIVERSITY OF MINNESOTA, MORRIS
MORRIS, MN 56267
NAME:.........................................................................
ID #:............................................................................
THE EXAM WAS ...........EASY ..........FAIR ..........DIFFICULT
FOR INSTRUCTORS USE
1. a......./4 b......./3 c......./8 d......./10
........../25
2. a......../10 b......./10
........../20
3. a......./8 b......./7
........../15
4. a......./8 b......./12
........../20
5. a......./8 b......./12
........../20
TOTAL ........../100
1. The following are the street prices of the top 20 budget desktops (PC WORLD online, 10/15/97).
|
WITH MMX |
|
WITHOUT MMX |
||
|
System |
Street Price($) |
|
System |
Street Price($) |
|
Dell Dimension |
1829 |
|
Quantex QP6 |
2399 |
|
Quantex QP5 |
1849 |
|
Polywell |
1295 |
|
Gateway 2000 |
1899 |
|
Micro Express K5 |
1299 |
|
Kingdom 200 |
1997 |
|
Cyber Max Power Max |
1599 |
|
ProGen Atlas |
1729 |
|
USA Flex Performer |
1999 |
|
Micro Express-P5 |
1699 |
|
Micro Express-PR |
1849 |
|
Cyber Max P200 |
1749 |
|
Kingdom P166 |
1197 |
|
Nexar |
1659 |
|
Micro Express LC |
1799 |
|
Poywell Poly |
1785 |
|
Micro Express PCI |
1799 |
|
Royal |
1799 |
|
ProGen Discover |
1149 |
a. Describe the population(s) of interest.
b. What is the variable of interest. Is this data qualitative or quantitative?
c. Produce a stem-and leaf display for the systems without MMX.
d. Construct side-by-side boxplot for the data by separating the systems with and without MMX and interpret it.
2. According to data from A. C. Nielsen, Americans spent an average of $36.32 per pair of sneakers between October 1994 and September 1995 (American Demographics, March 1996). assume that the purchase prices of all sneakers bought by Americans have a mean of $36.32 and a standard deviation of $8.00.
a. Find at least what percentage of all sneaker purchase prices are between 12.32 and 60.32.
b. Suppose that sneaker purchase prices is mound-shaped. Approximately what percentage of all sneaker purchase prices will be
I. between $20.32 and $52.32
II. less than $20.32.
3. Investing is a game of chance. Suppose there is a 40% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so high, you decide to invest in four independent risky stocks.
a. What is the probability that all four stocks end up in total loss?
b. What is the probability that at least one of the stocks end up in total loss?
4. Five hundred women and men were asked whether or not they would marry their current spouses if they were given a chance to do it over again. Their responses are recorded in the following table.
|
|
Would Marry the Current Spouse |
|
|
|
Yes(Y) |
No(N) |
|
Female(F) |
55 |
145 |
|
Male(M) |
125 |
175 |
a. If one person is selected at random from these 500 persons, find the following probabilities
I. Yes given female
II. Female given Yes
III. Yes or Female
b. Are the events "male" and "yes" independent? Explain why or why not.
5. Consider the two systems of components connected as in the accompanying pictures. The probability of failure for components in the System I is 0.2. Assume components operate independently of each other.
a. Find the probability that the System I operates properly.
b. If the probability that the System II operates properly is the same as System I, what is the probability of failure for components in the System II?
(Note that failure probabilities for the components in the System II are the same)