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The 68-95-99.7 Rule (also called the EMPIRICAL RULE): A Normal distribution is a collection of many data points that form a bell shaped curve. Note: x = mean s.d. = standard deviation Approximately __________ of the observations fall within _______________ of the mean _____. Approximately __________ of the observations fall within _______________ of the mean _____. Approximately __________ of the observations fall within _______________ of the mean _____. 1. Determine the percentages of data of the standard Normal curve between each value: a. Between mean ( x ) and 1 standard deviation: b. Between +1 standard deviation and +2 standard deviation: c. Between -3 standard deviation and –1 standard deviation: 2. The heights of students are approximately normal with a mean of 66” and a standard deviation of 3”. Label the Normal curve: What conclusions can you draw about the heights of the students? 1. ________________________________________________________________________________________________ 2. ________________________________________________________________________________________________ 3. ________________________________________________________________________________________________ Maria’s spelling bee scores follow a Normal distribution with a mean of 83 points and a standard deviation of 10.6 points. (a) What are the values of Maria’s selling bee scores that are 1 standard deviation from the mean? (b) What are the values of Maria’s selling bee scores that are 2 standard deviations from the mean? (c) What are the values of Maria’s selling bee scores that are 3 standard deviations from the mean? (d) What percent of the spelling bee scores fall between _____ and _____? (answers from part a) (e) What percent of the spelling bee scores fall between _____ and _____? (answers from part b) (f) What percent of the spelling bee scores fall between _____ and _____? (answers from part c) Label the Normal curves for Maria and Heidi: Heidi’s spelling bee scores follow a Normal distribution with a mean of 83 points and a standard deviation of 16.8 points. (a) What are the values of Heidi’s selling bee scores that are 1 standard deviation from the mean? (b) What are the values of Heidi’s selling bee scores that are 2 standard deviations from the mean? (c) What are the values of Heidi’s selling bee scores that are 3 standard deviations from the mean? (d) What percent of the spelling bee scores fall between _____ and _____? (answers from part a) (e) What percent of the spelling bee scores fall between _____ and _____? (answers from part b) (f) What percent of the spelling bee scores fall between _____ and _____? (answers from part c) ADD THE DOT PLOTS ONTO THE NORMAL CURVES FOR MARIA & HEIDI’S SCORES.