Standard Normal Distribution The Classic BellShaped curve is

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Standard Normal Distribution The Classic Bell-Shaped curve is symmetric, with mean = median =

Standard Normal Distribution The Classic Bell-Shaped curve is symmetric, with mean = median = mode = midpoint

Standard Normal Distribution

Standard Normal Distribution

Probabilities in the Normal Distribution The distribution is symmetric, with a mean of zero

Probabilities in the Normal Distribution The distribution is symmetric, with a mean of zero and standard deviation of 1. The probability of a score between 0 and 1 is the same as the probability of a score between 0 and – 1: both are. 34. Thus, in the Normal Distribution, the probability of a score falling within one standard deviation of the mean is. 68.

More Probabilities The area under the Normal Curve from 1 to 2 is the

More Probabilities The area under the Normal Curve from 1 to 2 is the same as the area from – 1 to – 2: . 135. The area from 2 to infinity is. 025, as is the area from – 2 to negative infinity. Therefore, the probability that a score falls within 2 standard deviations of the mean is. 95.

Normal Distribution Problems Suppose the SAT Verbal exam has a mean of 500 and

Normal Distribution Problems Suppose the SAT Verbal exam has a mean of 500 and a standard deviation of 100. Joe wants to be accepted to a journalism program that requires that applicants score at or above the 84 th percentile. In other words, Joe must be among the top 16% to be admitted. What score does Joe need on the test?

To solve these problems, start by drawing the standard normal distribution. Next, formula for

To solve these problems, start by drawing the standard normal distribution. Next, formula for z:

Next: Label the Landmarks z. X – 2 – 1 0 1 2 X

Next: Label the Landmarks z. X – 2 – 1 0 1 2 X 300 400 500 600 700

Now Check the Normal Areas We now know that: 2. 5% score below 300;

Now Check the Normal Areas We now know that: 2. 5% score below 300; i. e. , z = – 2 16% score below 400 50% score below 500; i. e. , z = 0 84% score below 600 97. 5% score below 700; i. e. , z = 2

Solution Summary Joe had to be among the top 16% to be accepted. That

Solution Summary Joe had to be among the top 16% to be accepted. That means his z-score must be +1. Thus, his raw score must be at least 600, which is one standard deviation (100) above the mean (500). Therefore, Joe needs to score at least 600.

Next Topic: Correlation We have seen that the z-score transformation allows us to convert

Next Topic: Correlation We have seen that the z-score transformation allows us to convert any normal distribution to a standard normal distribution. The z-score formula is also useful for calculating the correlation coefficient, which measures how well one can predict from one variable to another, as you learn in the next lesson.