Critical Thinking
Skills: Analyzing continuous data, understanding probability density functions, applying distributions to solve problems.
Application: Students will critically evaluate different types of continuous data and apply the appropriate probability distributions to model real-world situations.
Communication
Skills: Explaining statistical concepts, presenting data analysis, articulating the use of probability distributions.
Application: Students will communicate their understanding through presentations and written reports that explain their use of continuous probability distributions.
Collaboration
Skills: Working in groups, sharing insights, discussing and applying statistical methods.
Application: Students will collaborate on projects that require the application of continuous probability distributions to real-world data, enhancing their teamwork and problem-solving skills.
Skills
Interpreting data from continuous probability density functions.
Calculating probabilities using the uniform, exponential, normal, and standard normal distributions.
Modeling real-world phenomena using continuous probability distributions.
Comparing normal probabilities by converting to the standard normal distribution.
Communicating statistical findings effectively.
 What are continuous probability density functions, and how do they differ from discrete probability distributions?
How are the uniform probability distribution and exponential probability distribution described and modeled and how can they be used to model time-dependent events?
How do we recognize and apply the normal and standard normal probability distributions in real-world scenarios?
Recognize and understand continuous probability density functions in general.
Identify and apply the uniform, exponential, and normal probability distribution appropriately.
Compare normal probabilities by converting to the standard normal distribution.
Interpreting data from continuous probability density functions.
Calculating probabilities using the uniform, exponential, normal, and standard normal distributions.
Modeling real-world phenomena using continuous probability distributions.
Comparing normal probabilities by converting to the standard normal distribution.
Communicating statistical findings effectively.
Common Core Standards for Probability & Statistics:
CCSS.Math.Content.HSS.ID.A.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.
CCSS.Math.Content.HSS.MD.A.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution.
CCSS.Math.Content.HSS.MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Textbook: OpenStax Introductory Statistics
Online Courses: Khan Academy Statistics and Probability
Tools: Stat Trek Probability Calculator
Simulations: Probability Simulations
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