1. A 1 m3 sample of moist soil weighs 2000 kg. The water content is 10%. Assume s
is 2.70 Mg/m3. With this information, fill in the blanks in the phase diagram.
2. The dry density of a soil is 1.65 Mg/m3 and the solids have a density
Most of the optimization problems considered
to this point have had a single objective.
Two other modeling techniques:
Goal Programming (GP): no one specific objective
function but r
When one or more variables in an LP problem
must assume an integer value we have an
Integer Linear Programming (ILP) problem.
ILPs occur frequently
Integer variables als
2. Let X = no. of customers who purchased a particular coupon special
N = 2000
n = 50
X = 894.50
unknown population distribution of X
n = 50 > 30 Central Limit Theorem
Sampling distribution of is approximately normal.
1. An orange juice producer buys all his oranges from a large orange orchard. The
amount of juice squeezed from each of these oranges is assumed to be normally
distributed with a mean of 4.70 ounces and a standard deviation of 0.40 ounce.
Confidence Interval Estimation
There are two types of estimates for unknown population parameters:
1. Point estimate: consists of a single sample statistic value which is used to estimate the
true population parameter value.
2. Interval estimate
QMDS SATISTICS AND DATA ANALYSIS
Assignment # 3
Textbook, Problem 8.47, p.307
Let X = number of companies that informally monitored social networking sites to stay
on top of information related to their company
n = 500
p = 500 =
Fundamentals of Hypothesis Testing: One-Sample Tests
Hypothesis testing is a procedure based on sample evidence and probability theory to
determine whether the hypothesis is a reasonable statement and should not be rejected, or
is unreasonable a
1. A representative of a community group claims that the average income per
household in the area is $25,000. Suppose that for the type of area involved
household income can be assumed to be approximately normally distributed, and
the standard d
1. Let X = household income
1 = first community
2 = second community
H0: 1 2 = 0
H1: 1 2 0
Both population distributions are normal Sampling distribution of ( X 1 X 2 ) is normal.
n1 = 30 & n 2 = 40
X 1 = 35500 & X 2 = 34600
1. A developer is considering two alternative sites for a regional shopping center.
Since household income in the community is one important consideration in such
site selection, he wishes to perform the test that there is no difference between
Two-Sample Tests and One-Way ANOVA
In Topics 8 and 9, we learned how to obtain confidence intervals and perform hypothesis tests for one population parameter (, , or 2).
Frequently, however, inferential statistics is used to compare the paramet
1. Let X = income per household in the area
H0: = 25000
n = 15
Population distribution of X is normal.
Sampling distribution of is normal.
Test statistic: Z STAT =
Decision rule: Reject H0 if ZSTAT
QMDS200 STATISTICS AND DATA ANALYSIS
Assignment # 3
Please put the course code, section number, course title, student name and student number on
the top left corner of the first page.
In order to obtain full marks, please show all calculations and steps l
CHAPTER 1 THE MANUFACTURING SYSTEM
an industrial activity that
changes the form of raw materials
to create products.
Manufacturing system established by an enterprise,
facilitate the flow of information
/ Economic, Environmental, and
Societal Issues in Materials
Science and Engineering
sed aluminum beverage
cans that are to be recycled.
These cans will be crushed
and pressed into bales (shown
in the background) and then
shredded into small p
/ Phase Diagrams
scanning electron micro-
graph which shows the microstructure of a plain carbon
steel that contains 0.44 wt%
C. The large dark areas are
proeutectoid ferrite. Regions
having the alternating light
and dark lamellar structure
hotograph of a steel gear that
has been case hardened. The outer
surface layer was selectively
hardened by a high-temperature
heat treatment during which carbon
from the surrounding atmosphere
diffused into the surface. The case
familiar item that is fabricated from three different material types is the beverage
container. Beverages are marketed in aluminum (metal) cans (top), glass (ceramic) bottles (center), and plastic (polymer) bottles (bottom). (Pe
C01S01.001: If f (x) = 1 , then: x 1 1 (a) f (-a) = =- ; -a a 1 (b) f (a-1 ) = -1 = a; a 1 1 (c) f ( a ) = = 1/2 = a-1/2 ; a a (d) f (a2 ) = 1 = a-2 . a2
C01S01.002: If f (x) = x2 + 5, then: (a) f (-a) = (-a)2 + 5 = a2 + 5; (b) f (a-1 ) = (a-1