In a time before calculators…

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Presentation transcript:

In a time before calculators… EQ: What is a Z-table and what do I do with it?

Z-tables Finds the percent under the curve to the left of a given z- score. The body of the table contains the percentages, the row and column labels tell about the z-score.

First 2 digits of z-score Probability of a values less than a given z-score Third digit of z-score probabilities First 2 digits of z-score

Using the z-table Michael Jordan had a z-score of 3.2. How many people are his height or smaller? Find the 3.2 row. Find the .00 column P(z < 3.2) = .9993 Michael Jordan is taller than 99.93 percent of males.

Use the z-table to find the proportion Mugsy Bogues is 63 in. tall. What percent of people are taller than him? Recall men’s heights: N(69,2.8) Find his z-score. Use the z-table to find the proportion P(z < -2.14) = .0162 P(z > -2.14) = 1 -.0162 = .9838

Example IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 152. How many points away from the mean is Einstein? How many deviations away from the mean is Einstein? What is the z-score for his IQ? Any IQ outside of 2 deviations from the mean is considered unusual. Is Einstein’s IQ unusual? What percentile is Albert Einstein in for his IQ? 70, 3.25, 3.25, unusual, 0.9994

Example The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution: What is the probability of getting a raw score between 28 and 38? What is the probability of getting a raw score between 41 and 44? What number represents the 65th percentile (what number separates the lower 65% of the distribution)? What number represents the 90th percentile? 57%, 9%, 37.31, 42.71