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Sec. 5.1-5.2 Introduction to Normal Distributions
Mr. Ricks Madison High School
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Properties of a Normal Distribution
The mean, median, and mode are equal The normal curve is bell-shaped and symmetric about the mean The total area under the curve is equal to one (more about this in a minute) We can apply the Empirical Rule
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Which normal curve has a greater mean? Standard deviation?
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Adult IQ scores are normally distributed with 𝑥 =100 𝑎𝑛𝑑 𝑆 𝑥 =15
Adult IQ scores are normally distributed with 𝑥 =100 𝑎𝑛𝑑 𝑆 𝑥 =15. Estimate the probability that a randomly chosen adult has an IQ between 70 and 115. How many adults in a sample of 1000 would be expected to have an IQ between 70 and 115? Estimate the probability that a randomly chosen adult has an IQ score between 85 and 145.
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The Standard Normal Distribution
Has a mean of 0 and a standard deviation of 1 The horizontal axis of the graph corresponds to z-scores Do you remember how to calculate a z-score?
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Properties of the Standard Normal Distribution
The cumulative area is close to 0 for z-scores close to -3.49 The cumulative area increases as the z-scores increase The cumulative area for z=0 is The cumulative area is close to 1 for z-scores close to 3.49
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Using the Standard Normal Table
Refer to the table on the inside front cover of our text
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Find the area under the curve to the left of a z-score of -2.19
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Find the area under the curve to the left of a z-score of 2.34
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The Standard Normal Distribution Table can be used to easily find the area…
to the left of a z-score (find value in table) to the right of a z-score (find value in table and subtract it from 1) between 2 z-scores (find each value and subtract the smaller from the larger)
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Find the area under the standard normal curve…
to the right of 2.57 between and -1.35 0.0051 0.0731
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Finding Area on the TI-84 Press 2nd DISTR 2
Enter values for lower and upper z-scores Use –1E99 for lower limit if you’re finding area to the left of a z-score Use 1E99 for upper limit if you’re finding area to the right of a z-score
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Find the area under the standard normal curve…
to the left of to the left of 2.34 to the right of 2.57 in between and -1.35
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Sec. 5.1-5.2 Pg. 210 #6-10,13-14,17-22,23,25,27 (16) Pg. 219 #1,4,5-8,9-35(odd), 37-40 (24)
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