Since the total area under any normal curve is 1, it follows that the areas on either side of z = 0 are both 0.5. Since normal curves are symmetric about their mean, it follows that the curve of z scores must be symmetric about 0. Part (c) above illustrates how z-scores become crucial when you want to compare distributions.Note that even though Ross’ foot is longer than Candace’s, Candace’s foot is longer relative to their respective genders. Ross: z-score = (13.25 – 11) / 1.5 = 1.5 (Ross’ foot length is 1.5 standard deviations above the mean foot length for men).Ĭandace: z-score = (11.6 – 9.5) / 1.2 = 1.75 (Candace’s foot length is 1.75 standard deviations above the mean foot length for women). To answer this question, let’s find the z-score of each of these two normal values, bearing in mind that each of the values comes from a different normal distribution. Which of the two has a longer foot relative to his or her gender group? Ross’ foot length is 13.25 inches, and Candace’s foot length is only 11.6 inches. Assume that women’s foot length follows a normal distribution with a mean of 9.5 inches and standard deviation of 1.2. (c) In general, women’s foot length is shorter than men’s. Note that z-scores also allow us to compare values of different normal random variables. Since the mean is 11, and each standard deviation is 1.5, we get that the man’s foot length is: 11 + 2.5(1.5) = 14.75 inches. If z = +2.5, then his foot length is 2.5 standard deviations above the mean. What is his actual foot length in inches? (b) A man’s standardized foot length is +2.5. This foot length is 1.67 standard deviations below the mean. (a) What is the standardized value for a male foot length of 8.5 inches? How does this foot length relate to the mean? Details for Non-Parametric Alternatives in Case C-Q.Unit 4A: Introduction to Statistical Inference.Summary (Unit 3B – Sampling Distributions).Sampling Distribution of the Sample Mean, x-bar.Sampling Distribution of the Sample Proportion, p-hat.Conditional Probability and Independence.
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Linear Relationships – Linear Regression.Standard Normal Distribution » Biostatistics » College of Public Health and Health Professions » University of Florida