Section 5.3
Summer 2013 - Math 1040
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Roadmap
This chapter allows us to start with a percentageof area under the normal
curve, and then find a z-score. Then we can find an x-value that
corresponds to that z-score.
x =µ+z ·σ
Go from an area to a z-score.
Go from a z-score to an x-value.
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Percentiles
Percentiles are percentages of cumulative areas under a normal curve.
Using the standard normal curve, we can find z-scores the correspond to
percentiles.
Example The 42nd percentile, P42 is the z-score, or closest z-score, to the
area value of 0.4200. The table gives us 0.4207. It z-score is -0.20.
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Quartiles
The first and third quartile are the z-scores corresponding to 25% and
75%, respectively.
Note that for P25 = −0.675, its oppostite is +0.675, or P75 . This is
because the standard normal curve has a mean of 0 and is symmetric.
What is P50 ?
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Find an x-value
Using the z-score formula, solved for x:
x =µ+z ·σ
we can find specific values that match a given percent.
Example Find the upper 6-percentile for a distribution of cat weights with
µ = 9 and σ = 2.
The z-score for 0.9400 is 1.55.
x = 9 + 1.55 × 2 = 12.1 lbs
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Assignments
Assignment:
1
Read pages 257 - 261
Vocabulary: No new vocabulary.
Understand: Find a z-score given an area or probability. Transform a
z-score into an x-value.
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