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Math III: Z-Score and Empirical Rule Name ___________________________________________ Characteristics of a Normal Distribution: 1. ______________________________________________ 2. _______________________________________________ 3. ___________________________________________________________________________________ Mean Normal Distribution Mean = ______________________________________________________________________________ Standard Deviation = measures ___________________________________________________________________________________________. A low standard deviation indicates that the data points tend to be very _____________ to the mean (also called expected value); A high standard deviation indicates that the data points are _____________________________________________. The Normal Distribution Curve: All normal distributions will be ___________________________ The area under the curve represents the count of items at that Ο= value. What value has the most? ________________! Notice that itβs symmetric over the_______________, there are the same about above and below. -3 -2 -1 0 1 2 3 Here we are told the standard deviation is 1. Each integer is one ΞΌ= standard deviation away. The z-score is the number of ____________________________ a value is from the _____________________________. What is the z-score of the value indicated on the curve? 1. 2. 3. Precise formula for finding a z-score: Meaning of a positive z-score? Meaning of a negative z-score? π§= In statistics, the β68β95β99.7β rule, also known as the Empirical Rule, ________________________________________ _________________________________________________________________________________________________. ______________ % falls within ± 1Ο ________________% falls within ± 2Ο ______________% falls within ± 3Ο How do we use the empirical rule? The scores on the Math 3 midterm were normally distributed. The mean is 82 with a standard deviation of 5. Create and label a normal distribution curve to model the scenario. Hint: Draw the curve, add the mean, then add the standard deviations above and below the mean. Find the probability that a randomly selected person: a. scored between 77 and 87 d. scored higher than 92 b. scored between 82 and 87 c. scored between 72 and 87 e. scored less than 77