Sec. 5.1-5.2 Introduction to Normal Distributions Mr. Ricks Madison High School

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

Which normal curve has a greater mean? Standard deviation?

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.

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?

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 0.5000 The cumulative area is close to 1 for z-scores close to 3.49

Using the Standard Normal Table Refer to the table on the inside front cover of our text

Find the area under the curve to the left of a z-score of -2.19

Find the area under the curve to the left of a z-score of 2.34

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)

Find the area under the standard normal curve… to the right of 2.57 between -2.16 and -1.35 0.0051 0.0731

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

Find the area under the standard normal curve… to the left of -2.19 to the left of 2.34 to the right of 2.57 in between -2.16 and -1.35

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)