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# s_m6 - STA 2023 Module 6 The Normal Distribution Learning...

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STA 2023 Module 6 The Normal Distribution

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Learning Objectives Upon completing this module, you should be able to: 1. Explain what it means for a variable to be normally distributed or approximately normally distributed. 2. Explain the meaning of the parameters for a normal curve. 3. Identify the basic properties of and sketch a normal curve. 4. Identify the standard normal distribution and the standard normal curve. 5. Determine the area under the standard normal curve. 6. Determine the z-score(s) corresponding to a specified area under the standard normal curve. 7. Determine a percentage or probability for a normally distributed variable. 8. State and apply the 68.26-95.44-99.74 rule. 9. Explain how to assess the normality of a variable with a normal probability plot. 10. Construct a normal probability plot. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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The Standard Deviation as a Ruler The trick in comparing very different-looking values is to use standard deviations as our rulers. The standard deviation tells us how the whole collection of values varies, so it’s a natural ruler for comparing an individual to a group. As the most common measure of variation , the standard deviation plays a crucial role in how we look at data. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
Standardizing with z -scores We compare individual data values to their mean , denoted as µ , relative to their standard deviation , denoted as σ , using the following formula: z = (x - µ)/σ We call the resulting values standardized values , denoted as z . They can also be called z -scores . http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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Standardizing with z -scores (cont.) Standardized values have no units. z -scores measure the distance of each data value from the mean in standard deviations. A negative z -score tells us that the data value is below the mean, while a positive z -score tells us that the data value is above the mean. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
Standardizing Values Standardized values have been converted from their original units to the standard statistical unit of standard deviations from the mean . Thus, we can compare values that are measured on different scales, with different units, or from different populations. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.

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Shifting Data Shifting data : Adding (or subtracting) a constant to every data value adds (or subtracts) the same constant to measures of position. Adding (or subtracting) a
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s_m6 - STA 2023 Module 6 The Normal Distribution Learning...

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