1
1.
Use the sales forecasters predication to describe a normal probability distribution that can be used to
approximate the demand distribution. Sketch the distribution and show its mean and standard
deviation.
As per given information with 95% probabili
Case Problem 2 Gulf Real Estate Properties
Gulf Real Estate Properties, Inc., is a real estate firm located in southwestern Florida. The
company, which advertises itself as “expert in the real estate market,” monitors condo
minium sales by collecting dat
Eureka Consultants
Heavenly Chocolates ERetail Business Report
Prepared by Eureka Consultants
Date: 29 September 2015
Rahul Rathod & Yuan Gao
THE GEORGE WASHINGTON UNIVERSITY
0
Eureka Consultants
Table of Contents
1. Introduction
2
2. Analysis of online
DNSC 6202 Practice Assignment
Prepared by:
Rahul Rathod
Yuan Gao
September 5th 2015
1. Define the terms managerial science and operations research.
Both are rational approaches to decision making based on scientific method.
Managerial science refers to th
Density Curves and the
Normal Distribution
NORMAL DISTRIBUTION
Density Curves
Density curve is a curve that is
(a) is always above the xaxis(horizontal axis)
(b) Has total area under the curve to be 1.
It describes the overall pattern of distribution
Ar
A Complete Example
The dataset gives ammonia level near an
exit ramp of a tunnel tunnel for 8 different
days
cfw_1.53, 1.50, 1.37, 1.51,
1.55, 1.42, 1.41, 1.48
Mean and SD
Obs
1.53
2
Deviation Deviation2
.05875
.00345
1.50
1.37
.02875
.00083
x = 1.47125

The Empirical Rule (689599.7 rule)
Sometimes the distribution is symmetric and bell
shaped. For these kind of distribution mean and
sd together can describe the distribution fairly
well.
Most of the observations lie near the center or
mean of the data.
Comparing Mean, Median and Mode
For negatively (left) skewed distributions
Mean < Median < Mode
Mean
Mode
Median
1
Skewed Right
For positively skewed distributions
Mean > Median > Mode
Mode
Mean
Median
2
Symmetric Distribution
For symmetric (not skewed) d
Descriptive Statistics
Numerical Summary
Summation Notation
Observations in a dataset are denoted by
cfw_ x1,x2,x3,x4,.xn ; n = sample size
x1 is the first observation, x2 is 2nd obs. and so
on.
We use xi to denote x1 + x2 + x3 + x4 +.+ xn
In particula
Descriptive Statistics
Numerical Summary
Summation Notation
Observations in a dataset are denoted by
cfw_ x1,x2,x3,x4,.xn ; n = sample size
x1 is the first observation, x2 is 2nd obs. and so
on.
We use xi to denote x1 + x2 + x3 + x4 +.+ xn
In particula
Frequency Distribution
Dataset is summarized in a tabular form.
Range of the dataset is partitioned into a number
of classes of equal width.
Frequency distribution table is constructed by
counting number of observations (called
frequency) in each class an
Descriptive Statistics
Quantitative Data
Quantitative Data
Measurements that can be measured on a
natural and meaningful numerical scale
Examples:
a)
b)
c)
SAT score of students
The current unemployment rate for 50 states
Number of calls made over last we
Chapter 1
Descriptive Statistics
Contents
Introduction
Qualitative Data
Frequency Distribution
Graphical Methods
Quantitative Data
Graphical Methods
Numerical Summary
Box Plot
2
Qualitative Data
Measurements that cannot be measured on a
natural num
Confidence Intervals
Population Mean: Small Sample
Confidence Interval for :
Small Samples
In many cases, sample sizes may be small
(n <30) and the population standard
deviation may be unknown (usually that
is the case).
Confidence Interval
Some Reasons:
Confidence Interval
Estimating the Mean: Large
Sample
1
Example 1.0:
The seasonal rainfall in a county in
California, when observed over sixteen
randomly picked years, yielded a mean
rainfall of 20.8 inches. From the past
experience, rainfall during a sea
Chapter 6
Confidence Intervals
Contents
Notations
Statistical Inference
Confidence Interval For Population Mean
Large Sample
Small Sample
Confidence Interval For Proportion
Large Sample
Sample Size Determination
2
Inferential Statistics
INFERENTIA
Normal Distribution
Normal Distribution
(Continued)
Example 8.0
Find the real number a in each of the following cases.
a) P(0 < Z < a) = 0.1915
b) P(Z < a) = 0.9821
c)
P(a < Z < a) = 0.6826
Remark: Note that we can use the normal tables to find
the appro