What if we are given a probability and want to find a value?
Remember that normal probabilities are probabilities that a random
value x falls in a given interval.
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Intervals will be phrased like, ”top 10%,” or, ”middle 70%.”
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Use the probability given to find the z-score with the standard
normal table. This is called a percentile.
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Transform the z-score to a data value x using
Notes
x =µ+z ·σ
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Be sure to draw the normal distribution curve!
Example - Table Basics
Notes
Find the z-score that correspond to each percentile.
1. P5 (5% of the distribution’s area is to the left)
2. P20 (20% of the distribution’s area is to the left)
3. P90 (90% of the distribution’s area is to the left)
Finding x-values
A veterinarian records the weights of cats treated at a clinic. The
weights are normally distributed with a mean of 9 pounds and a
standard deviation of 2 pounds. Find the weights x that correspond
to z-scores of 1.96, -0.44, and 0. Interpret the results in the real-life
context.
Notes
Finding a specific x-value
Notes
The braking distance of a sample of Nissan Altimas are normally
distributed, with a mean of 129 feet and standard deviation of 5.18
feet. What is the longest braking distance one of these Nissan
Altimas could have and still be in the bottom 10%?
Finding a specific x-value
Notes
The lengths of time employees have wored at a corporation are
normally distributed, with a mean of 11.2 years and a standard
deviation of 2.1 years. The company plans on cutbacks, and will lay
off a certain percentage of workers in senoirity. What is the maximum
length of time an employee could have worked and be layed off if the
company cuts back the lowest 15% in seniority?
Assignment
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§5.3: 33, 34, 36, 39
Suggested Exercises: 1, 5, 9, 13, 17, 19, 21, 23, 25, 27
Notes