Quiz 2
Chapters 4 & 5__TEAM A week 5________________________
1) Use the standard normal distribution to find P(2.25 < z < 1.25). A) .0122B) .8821C) .8944D) .4878
P(2.25 < z < 1.25) = F(1.25)  (1  F(2.25)) = 0.89435  (1  0.987776) = 0.882126
2) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $ 900 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, a. what is the probability that during a randomly selected month PCE's were between $775.00 and $990.00? A) .0421B) .0001C) .9999D) .9579
b. what is the probability that during a randomly selected month PCE's were between $375.00 and $590.00? A) .9579B) .9999C) 2.82316E10D) .0421
c Find the point in the distribution below which 2.5% of the PCE's fell. A) $ 682.50B) $ 602.00C) $ 802.00D) $ 17.50
3) The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 2.5 to 4.5 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 3.2 millimeters? A) 1.5B) 0.4571C) 0.7111D) 0.65
4) A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 12.5 gallons per minute.
a. What is the probability that at the time the machine is checked it is pumping more than 10.5 gallons per minute?
A) .50B) .25C) .7692D) .667
b. What is the probability that at the time the machine is checked it is pumping more than 9.0 gallons per minute? A) .7692B) .25C) .50D) .875
c. What is the probability that at the time the machine is checked it is pumping between 9.5and 10.5 gallons per minute?
...Pie Charts
An important part of decision making is having a clear understanding of the information used to base decisions from. Charts can be valuable when a need to represent numerical data would benefit communicating information visually. Some of the most important aspects of a good chart are to select the right type of chart (or graph) that can best characterize the data, also, to keep the design simple in order for an audience to easily understand the information.
One of the most popular types of charts is the pie chart. The pie chart is used to visually represent the proportional value of individual parts to the whole. As the name describes, this is done by representing the numerical equivalence of each part as a piece of the whole pie, which in total equates to 100%. The Pennsylvania Department of Health (2001) says that pie charts are a good choice when a relatively small amount of parts, perhaps 3 to 7, need to be represented. With any more it becomes difficult to notice the differences in magnitude; thus, the pie chart loses its simplicity and impact. They can only be used when a total amount is known, one such example would be an election where the total of votes received by all candidates equals 100% of the votes. Or a budget where the total amount spending is divided in to categories such as labor, facilities costs, advertising, etc ...
...Pareto Principle. Pareto charts provide facts and insights necessary for setting priorities. Pareto charts assist teams to focus on the smaller number of the causes of problems in order to aid in decision making. Pareto charts organize and display information. They are a form of vertical bar chart. Attributes are discussed. Suggestions on when to use a Pareto chart are made. Pareto analysis is one way to determine major causes of particular problems. A review is provided with suggestions for alternatives. The Pareto chart is a valuable decision making tool.
Tools & Techniques
Pareto Charts
As a decisionmaking tool, the Pareto chart provides facts and insights necessary for setting priorities. Vilfredo Pareto was an Italian economist credited with establishing what is now widely known as the Pareto Principle. It is also known as the "80/20 Rule" (iSixSigma, 2006). When Pareto discovered the principle in 1906, he established that 80% of the land in Italy was owned by 20% of the population. Later, Pareto discovered his principle was valid in other parts of his life, such as gardening. For example, 80% of his garden peas were produced by 20% of the peapods.
The "80/20 Rule is not literal. The ratios may vary. Rather than an even 80% to 20% ratio the exact percentage may be 82% to 18%, or 78% to 22%. However as a rule of thumb' it is common...
...Control Charts
Control Charts are use to distinguishes between specialcause or commoncause of variation that is present in a
process.
There are two basic types of control charts:
Variables

Quantitative data (Measured)
Attributes

Qualitative data (Counted)
Variable Control Charts
Use actual measurements for charting
Types:
Average & Range charts
Median & Range charts
Average & Standard deviation charts
Individual & Moving Range charts
Run Charts
Attribute Control Charts
Use pass/fail or go/nogo judgment
Types :p  chart
np  chart
c  chart
u  chart
OBJECTIVES OF VARIABLE CONTROL CHARTS
For quality improvement.
To determine the process capability.
For decisions in regard to product specifications.
For current decisions in regard to the production process.
For current decisions in regard to recently produced
items.
Average & Range charts ( and R)
Guidelines for subgroup sizes (n):
1.
As n increases the CL become closer to central line.
2.
As n increases the inspection cost per subgroup
increases.
3.
Distributions for averages of subgroups are nearly
normal for n = 4
4.
If n = 10 use the s chart instead of Rchart
5.
n =...
...
Statistical Analysis and Application of Charts
Presented To: Mam Ayesha IftikharPresented By: Hassan Bashir
Roll Number: bba02141016
Program : BBA
Semester : 2nd
Date: 19Oct2014
Research Questionnaire/ Objective:
Analysis of quantitative and qualitative data
Uses of appropriate charts under the specific/general scenario.
To ensure that statistical tools are the important for decision making.
Type of Data:
Quantitative Data
Qualitative data
Quantitative Data:
Quantitative data is data expressing a certain quantity, amount or range. Usually, there are measurement units associated with the data, e.g. meters, in the case of the height of a person.
Qualitative data:
Qualitative data is information about qualities; information that can't actually be measured. Some examples of qualitative data are the softness of your skin, the grace with which you run, and the color of your eyes. However, try telling Photoshop you can't measure color with numbers.
Charts:
Pie Chart
Line Chart
Histogram
FlowChart
Time Line Chart
5518206524001. Pie Chart:
A pie chart is divided into sectors, illustrating numerical proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. While it is named for its resemblance to...
...information is easily accessible to whoever needs it. If the data is unclear or ambiguous it is not fitforpurpose and is therefore redundant. When deciding on which methods to use, I was mindful of the audience and the information they needed. This information will be presented to senior managers as well as HR administrators so I have chosen to present my findings using methods that fulfil the requirements of all parties; spreadsheets (Appendix 1) and a pie chart and barchart (Appendix 2).
The spreadsheets contain detailed information and will be used to determine exactly who the affected NPL are. As I included the contract end date in this report, the data can be used to identify NPL who are nearing their 2 years of service and as a result may also be affected by the OCP.
As these extracted reports are quite complex, I’ve also chosen to illustrate the data visually using a bar chart and pie chart. Both are clear, concise and easy to analyse. The charts clearly show the variance in NPL and I used different colours on the pie chart so that the difference is even more distinguishable.
Now that I have provided the relevant information, the NPL workstream are able to make decisions regarding employing NPL in IM with more than 2 years’ service. I have presented the data using different methods to support this process and will make the team aware of the data limitations. One...
...Timeless Business Charts
Copyright 2013 Vishnuvarthanan Moorthy
Data speaks thousand words and Charts speak more than that! Are you one among them who are
interested in constructing fascinating charts, and do you believe management decisions can be done
easily with few interpretation of charts, then you can spend some “time” to read this…
Any activity/motion/process in this world not only consumes movement or energy, but they also
consume time. Traditionally we have been ignoring time, time and again. Unless we work on trend or
control charts we don’t represent time, instead we work to represent mostly the volume or results in
our charts without giving time scale to it. No result can be produced without time and time always
moves ahead and never comes back. Many a time it’s not a standard practice for us to attach or provide
details of time period of data along with any chart, and we require some manger with common sense to
ask the question, which time period it represents and what is the trend in this time period. If we look at
any output in chart, it’s important to ask the time it consumed/it represents in a chart. A better way of
representing is, every chart shall have time angle to it (only in trend/control charts and some or with
timeline). Today we miss time as an indicator in our charts,...
...Area Chart
Figure 1: Area chart
Use it to...
* Display over time (or any other dimension):
* How a set of data adds up to a whole (cumulated totals)
* Which part of the whole each element represents
Variants
* Percentage: The sum always represents 100% (relative scale)
* Cumulative: The sum can vary according to the elements (absolute scale)
Column/Bar Chart
Use it to...
* Present few data over a nominal (e.g. countries, testing conditions, ...) or interval scale (e.g. time); useful for comparisons of data
Do not Use it for...
* Comparisons: Better use onedimensional scatterplots, because these are not dominated by bars or columns.
* Larger data sets: Use line charts.
Selecting Bars or Columns
* Use analogy as a selection criterion, if applicable; when in doubt, use columns
* Use a horizontal bar chart if the labels are too long to fit under the columns
Variants
* Multiple Column/Bar Chart: Use it to present data rows for several variables
* SidebySide Chart: Use it to (1) show contrasting trends between levels of an independent variable, (2) if comparisons between individual pairs of values are most important; do not use for more than two independent variables
  
Figure 2: Multiple column chart (left), sidebyside chart (right)
Segmented Column/Bar...