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Winter Olympics 2010 speed skating The top 36 women’s
Chapter 5, Problem 9E(choose chapter or problem)
Winter Olympics 2010 speed skating The top 36 women’s 500-m speed skating times are listed in the table.
a) The mean finishing time was 40.44 seconds, with a standard deviation of 10.03 seconds. If a Normal model were appropriate, what percent of the times should be within 2 seconds of the mean?
b) What percent of the times actually fall within this interval?
c) Explain the discrepancy between parts a and b.
Questions & Answers
QUESTION:
Winter Olympics 2010 speed skating The top 36 women’s 500-m speed skating times are listed in the table.
a) The mean finishing time was 40.44 seconds, with a standard deviation of 10.03 seconds. If a Normal model were appropriate, what percent of the times should be within 2 seconds of the mean?
b) What percent of the times actually fall within this interval?
c) Explain the discrepancy between parts a and b.
Step 1 of 3
(a)
Given values
Mean \(\mu=40.44 \mathrm{sec}\)
Standard deviation, \(\sigma=10.03 \mathrm{sec}\)
To determine the percent of the times within 2 seconds of the mean, we will have to determine the z -score, ie;
\(z=\frac{x-\mu}{\sigma}=\frac{ \pm 2}{10.03}= \pm 0.2\)
From Table Z Appendix D, the area under the curve for z-score is between 0.4207 and 0.5793, ie;
0.5793 - 0.4207 = 0.1586
Therefore 15.86% of data should be within 2 seconds of the mean 40.44 sec.