Theoretical probability is calculated based on all possible outcomes, while experimental probability is calculated based on observed outcomes from an experiment. The document provides examples of calculating theoretical and experimental probabilities from sample spaces involving marbles drawn from a bag, student juice preferences in a class, movie preferences in surveys, and dice rolls. Probabilities are provided as fractions of possible outcomes.
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This powerpoint was used in my 7th and 8th grade classes to review the fundamental counting principle used in our probability unit. There are three independent practice problems at the end.
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
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Also, please do visit our page, LIKE and FOLLOW us on Facebook!
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This powerpoint was used in my 7th and 8th grade classes to review the fundamental counting principle used in our probability unit. There are three independent practice problems at the end.
History behind the
development of the concept
In 1654, a gambler Chevalier De Metre approached the well known Mathematician Blaise Pascal for certain dice problem. Pascal became interested in these problems and discussed it further with Pierre de Fermat. Both of them solved these problems independently. Since then this concept gained limelight.
Basic Things About The Concept
Probability is used to quantify an attitude of mind towards some uncertain proposition.
The higher the probability of an event, the more certain we are that the event will occur.
STATUse the information below to answer Questions 1 through 4..docxdessiechisomjj4
STAT
Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
1. What is the test statistic?
2. At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
3. What are the border values between acceptance and rejection of this hypothesis?
4. What is the power of this test if the assumed true mean were 710 instead of 700?.
Questions 5 through 8 involve rolling of dice.
5. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a “1” each time?
6. What is the probability of getting a “1” on the second roll when you get a “1” on the first roll?
7. The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1” when rolling this loaded die?
8. Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.
Use the data in the table to answer Questions 9 through 11.
x
3
1
4
4
5
y
1
-2
3
5
9
9. Determine SSxx, SSxy, and SSyy.
10.
Find the equation of the regression line. What is the predicted value when
11. Is the correlation significant at 1% significance level (99% confidence level)? Why or why not?
Use the data below to answer Questions 12 through 14.
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows:
Football
Basketball
Soccer
Maryland
60
70
20
Duke
10
75
15
UCLA
35
65
25
Supposed a student is randomly selected from the group mentioned above.
12. What is the probability that the student is from UCLA or chooses football?
13. What is the probability that the student is from Duke, given that the student chooses basketball?
14. What is the probability that the student is from Maryland and chooses soccer?
Use the information below to answer Questions 15 and 17.
There are 3600 apples in a shipment. The weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14 ounces with a standard deviation of 2.5 ounces.
15. How many of apples have weights between 13 ounces and 15 ounces?
16. What is the probability that a randomly selected mango weighs less than 12.5 ounces?
17. A quality inspector randomly selected 100 apples from the shipment.
a. What is the probability that the 100 randomly selected apples have a mean weight less than 12.5 ounces?
b. Do you come up with the same result in Question 16? Why or why not?
18. A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Un.
STATUse the information below to answer Questions 1 through 4..docxrafaelaj1
STAT
Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
What is the test statistic?
At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
What are the border values between acceptance and rejection of this hypothesis?
What is the power of this test if the assumed true mean were 710 instead of 700?
Questions 5 through 8 involve rolling of dice.
Given a fair, six-sided die, what is the probability of rolling the die twice and getting a “1” each time?
What is the probability of getting a “1” on the second roll when you get a “1” on the first roll?
The House managed to load the die in such a way that the faces “2” and “4” show up twice as frequently as all other faces. Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a “1” when rolling this loaded die?
Write the probability distribution for this loaded die, showing each outcome and its probability. Also plot a histogram to show the probability distribution.
Use the data in the table to answer Questions 9 through 11.
x
3
1
4
4
5
y
1
-2
3
5
9
Determine SS
xx
, SS
xy
, and SS
yy
.
Find the equation of the regression line. What is the predicted value when
Is the correlation significant at 1% significance level (99% confidence level)? Why or why not?
Use the data below to answer Questions 12 through 14.
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results, in number of students, are listed as follows:
Football
Basketball
Soccer
Maryland
60
70
20
Duke
10
75
15
UCLA
35
65
25
Supposed a student is randomly selected from the group mentioned above.
What is the probability that the student is from UCLA or chooses football?
What is the probability that the student is from Duke, given that the student chooses basketball?
What is the probability that the student is from Maryland and chooses soccer?
Use the information below to answer Questions 15 and 17.
There are 3600 apples in a shipment. The weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14 ounces with a standard deviation of 2.5 ounces.
How many of apples have weights between 13 ounces and 15 ounces?
What is the probability that a randomly selected mango weighs less than 12.5 ounces?
A quality inspector randomly selected 100 apples from the shipment.
What is the probability that the 100 randomly selected apples have a mean weight less than 12.5 ounces?
Do you come up with the same result in Question 16? Why or why not?
A pharmaceutical company has developed a screening test for a rare disease that afflicted 2% of the population. Unfortunately, the reliability of this test is only 80%, which m.
Stat 230 Summer 2014 – Final Exam Page 1 .docxdessiechisomjj4
Stat 230 Summer 2014 – Final Exam
Page 1
Please answer all 30 questions. Make sure your answers are as complete as
possible. Show all of your work and reasoning. In particular, when there are
calculations involved, you must show how you come up with your answers
with critical work and/or necessary tables. Answers that come straight from
program software packages will not be accepted.
You must include the Honor Pledge on the title page of your
submitted final exam. Exam submitted without the Honor
Pledge will not be accepted.
Honor Pledge: "I have completed this final examination myself, working independently
and not consulting anyone except the instructor. I have neither given nor received help on this
final examination."
Use the information below to answer Questions 1 through 3.
Given a sample size of 34, with sample mean 660.3 and sample standard deviation 104.9, we
perform the following hypothesis test. Since n>30, this is a Z test.
Null Hypothesis 0 : 700H
Alternative Hypothesis : 700aH
1. What is the test statistic? What is the p-value?
2. At a 5% significance level (95% confidence level), what is the critical value(s) in this
test? Do we reject the null hypothesis?
3. What are the border values of x between acceptance and rejection of this hypothesis?
Stat 230 Summer 2014 – Final Exam
Page 2
Questions 4 through 7 involve rolling of dice.
4. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a
“1” each time?
5. What is the probability of getting a “1” on the second roll when you get a “1” on the first
roll?
6. The House managed to load the die in such a way that the faces “2” and “4” show up
twice as frequently as all other faces. Meanwhile, all the other faces still show up with
equal frequency. What is the probability of getting a “5” when rolling this loaded die?
7. Write the probability distribution for this loaded die, showing each outcome and its
probability.
Use the data in the table to answer Questions 8 through 9.
x 3 1 4 4 5
y 2 -2 5 4 8
8. Determine SSxx, SSxy, and SSyy.
9. Find the equation of the regression line. What is the predicted value when 4?x
Stat 230 Summer 2014 – Final Exam
Page 3
Use the data below to answer Questions 10 through 12.
A group of students from three universities were asked to pick their favorite college sport
to attend of their choice: The results, in number of students, are listed as follows:
Football Basketball Soccer
Maryland 60 70 20
Duke 10 75 15
UCLA 35 65 25
Supposed that a student is randomly selected from the group mentioned above.
10. What is the probability that the student is from UCLA or chooses football?
11. What is the probability that the student is from Duke, given that the student chooses
basketball?
12. What is the probability that the .
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
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Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
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We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
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- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
JMeter webinar - integration with InfluxDB and GrafanaRTTS
Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
- Which features are provided by Grafana?
- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
8. In a survey, 100 people were asked to name their favorite Independence Day side dishes. What is the experimental probability of macaroni salad being someone’s favorite dish? 8 coleslaw 12 Macaroni salad 25 Green salad or vegetable 55 Potato salad Number of People Side Dish
9. Suppose 250 people attend the city’s barbecue. How many be expected to choose macaroni salad as their favorite side dish?
10. In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story , 15 chose The Ink Well , 10 chose The Monkey House , and 5 chose Little Rabbit . What is the experimental probability of someone wanting to see The Monkey House?
