9.2 Normal Probability Distribution
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Lab 9.2.1
In a standard normal distribution, where the mean is zero and standard deviation is one, what is the probability of obtaining a value (z -value) less than 1.5?
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Lab 9.2.2
The average college cost per year is $27191 with the standard deviation of $7126. Assume the distribution is normal.
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The lab's curve, with the boundary parked on the mean
The panel opens on N(27191, 7126) - the lab's own distribution - with the boundary sitting on the mean, where the area to the left is exactly 0.5. That is a check you can make without a calculator, and it confirms the two parameters went in correctly. Move the boundary to the cost the lab asks about and do the same calculation in Python; the two should agree to every digit.
Find the probability that a randomly selected college will cost less than $27726 per year.
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Inverse Normal
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Lab 9.2.3
The average college cost per year is $27,191 with standard deviation of $7,126. Assume the distribution is normal.
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Inverse mode, parked on the median
This link opens the same curve in Find x-Value (inverse) mode with the left-tail area set to 0.5, and it returns 27191 - the mean itself, because a normal distribution's 50th percentile IS its mean. Change the area to the percentile the lab asks for, then check it against stats.norm.ppf in your own cell.
Find the 75th percentile for this distribution
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Adapted from Python for Introductory Statistics: Student's Lab Workbook, by Simon Aman (Truman College, City Colleges of Chicago), licensed under CC BY 4.0. Changes were made: reformatted as an accessible XYZ web edition with live in-browser code cells. License: CC-BY-4.0 .
