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3-3 example15

# 3-3 example15 - Student Grady Simonton Course Math119...

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Unformatted text preview: Student: Grady Simonton Course: Math119: Elementary Statistics - Spring 2.010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 2/18/10 Book: Triola: Elementary Statistics, 11e Time: 1:52 PM Heights of men on a baseball team have a bell-shaped distribution with a mean of 185 cm and a standard deviation of 4 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 173 cm and 197 cm b.177 cm and 193 cm To determine the percent of the men between the given values, use the empirical rule. This rule states that for data sets having a distribution that is approximately bell-shaped, the following properties apply. - About 68% of all values fall within 1 standard deviation of the mean. - About 95% of all values fall within 2 standard deviations of the mean. - About 99.7% of all values fall within 3 standard deviations of the mean. Use the graph to the right to help you with the empirical rule. Note that it shows that 68% of data are within 1 standard deviation of the mean (i — s to i + s), 95% of data are within 2 standard deviations (x — 25 to x + 25), and 99.7% ofdata are within 3 standard deviations (; — 3s to i + 35). 34% 34% 2.4% 2.4% .10/ 1% x—3s x—Zs x—s X x+s X+Zs X+3S From the problem statement above, we know that the standard deviation, 5, is equal to 4 cm. To answer the questions, compute 2s and 3s. 2s=2(4)=8 3s=3(4)=12 a. To ﬁnd the percentage of the men between 173 cm and 197 cm, determine if these values are one, two, or three standard deviations from the mean. As shown below, 173 cm and 197 cm are 3 standard deviations from the mean. 185 — 12= 173 185 +12= 197 Therefore, according to the empirical rule, 99.7% of the men are between 173 cm and 197 cm. b. To ﬁnd the percentage of the men between 177 cm and 193 cm, determine if these values are one, two, or three standard deviations from the mean. As shown below, 177 cm and 193 cm are 2 standard deviations from the mean. 185 —8 = 177 185 +8= 193 Therefore, according to the empirical rule, 95% of the men are between 177 cm and 193 cm. Page 1 ...
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