Summary
Notes
Summary ideas from previous chapters:
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Plot data with a histogram.
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Finding the probability of an event.
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Interpreting ”unusual events” using the mean and standard
deviation.
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Find z-scores.
Key points of Chapter 5:
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Study and identify normal distributions (bell-shaped curves).
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Use properties of the mean and standard deviation of bell-shaped
curves.
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Convert data to standardized data (z-scores) and find
probabilities using a table.
A Normal Distribution
Notes
Continuous random variables have uncountably many outcomes. This
is represented by an interval on the number line.
Examples: Measurement of time (in minutes, hours, etc),
Measurements of volumes (gallons, cubic centimeters, etc),
Measurements of speed (miles per hour, etc), and like variables that
are measurements.
A normal distribution is a continuous probability distribution with a
symmetric and bell-shaped curve. The mean, median, and mode are
equal. One standard deviation away from the mean is where the curve
inflects from curving upward-to-downward, or curving from
downward-to-upward.
Same Mean
Curves can have the same mean, but different standard deviations.
µ1 = 3.5, σ1 = 1.5, and µ2 = 3.5, σ2 = 0.7
Notes
Different Mean
Notes
Curves can have the same standared deviations, but different means.
µ1 = 3.5, σ1 = 1.5 and µ2 = 1.5, σ2 = 1.5
The Standard Normal distribution
Notes
z-scores transforms any normal data into standard normal data.
z=
=
Value - Mean
Standard Deviation
x −µ
σ
For z-scores, round to the nearest hundreth.
Every normal distribution has its own mean and standard deviation.
The standard normal distribution has mean µ = 0 and standard
deviation σ = 1.
Assignment
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Read §4.1 to review continuous random variables (p 190 - 191),
and then all of §5.1.
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§5.1: 1, 2, 3, 4, 7, 9, 43, 44, 61
Try any of the exercises 25 to 38 for practice on using the table.
Exercises 51 to 60 are similar using a different style of notation.
Notes