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Assume college women have heights with the following distribution (inches): N(65, 2.8). Complete parts (a) through (d) below. ..... a. Find the height at the 75th percentile. The 75th percentile is. (Round to one decimal place as needed.) b. Find the height at the 25th percentile. The 25th percentile is. (Round to one decimal place as needed.) c. Find the interquartile range for heights. The interquartile range is (Round to one decimal place as needed.) d. Is the interquartile range larger or smaller than the standard deviation? The interquartile range is than the standard deviation.

Assume college women have heights with the following distribution (inches): N(65, 2.8). Complete parts (a) through (d) below. ..... a. Find the height at the 75th percentile. The 75th percentile is. (Round to one decimal place as needed.) b. Find the height at the 25th percentile. The 25th percentile is. (Round to one decimal place as needed.) c. Find the interquartile range for heights. The interquartile range is (Round to one decimal place as needed.) d. Is the interquartile range larger or smaller than the standard deviation? The interquartile range is than the standard deviation.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Assumption: College Women's Height Distribution** Assume college women have heights with the following distribution (inches): \(N(65, 2.8)\). Complete parts (a) through (d) below. --- **a. Find the height at the 75th percentile.** The 75th percentile is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **b. Find the height at the 25th percentile.** The 25th percentile is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **c. Find the interquartile range for heights.** The interquartile range is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **d. Is the interquartile range larger or smaller than the standard deviation?** The interquartile range is \(\_\_\_\_\_\) than the standard deviation. --- **Explanation:** - The distribution is normal with a mean (\(\mu\)) of 65 inches and a standard deviation (\(\sigma\)) of 2.8 inches. - To find percentiles and the interquartile range, use the properties of the normal distribution. - Compare the interquartile range with the standard deviation to determine their relative sizes.
Transcribed Image Text:**Assumption: College Women's Height Distribution** Assume college women have heights with the following distribution (inches): \(N(65, 2.8)\). Complete parts (a) through (d) below. --- **a. Find the height at the 75th percentile.** The 75th percentile is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **b. Find the height at the 25th percentile.** The 25th percentile is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **c. Find the interquartile range for heights.** The interquartile range is \(\_\_\_\_\). *(Round to one decimal place as needed.)* --- **d. Is the interquartile range larger or smaller than the standard deviation?** The interquartile range is \(\_\_\_\_\_\) than the standard deviation. --- **Explanation:** - The distribution is normal with a mean (\(\mu\)) of 65 inches and a standard deviation (\(\sigma\)) of 2.8 inches. - To find percentiles and the interquartile range, use the properties of the normal distribution. - Compare the interquartile range with the standard deviation to determine their relative sizes.
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