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 bellshaped 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 bellshaped, 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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 Spring '10
 PARVINI

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