Problem #2. Suppose that a category of world class runners are known to run a Spartathlon, a 246-kilometer (153 mi) ultramarathon race in an average of 26 hours with a standard deviation of 3 hours. Consider 36 of the races. Let X the average of the 36 races. Explain or show work for all part of the question. A. In words, X = B. X - C. Find the IQR for the average finishing time in these 36 races. D. Find the probability that the runner will average in under 24 hours in these 36 races. E. How many races should be considered if we want the standard deviation of X to be half (1.5 hours) of the standard deviation given in the problem.
Problem #2. Suppose that a category of world class runners are known to run a Spartathlon, a 246-kilometer (153 mi) ultramarathon race in an average of 26 hours with a standard deviation of 3 hours. Consider 36 of the races. Let X the average of the 36 races. Explain or show work for all part of the question. A. In words, X = B. X - C. Find the IQR for the average finishing time in these 36 races. D. Find the probability that the runner will average in under 24 hours in these 36 races. E. How many races should be considered if we want the standard deviation of X to be half (1.5 hours) of the standard deviation given in the problem.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**Problem #2.** Suppose that a category of world class runners are known to run a *Spartathlon*, a 246-kilometer (153 mi) ultramarathon race in an average of 26 hours with a standard deviation of 3 hours. Consider 36 of the races. Let \( \overline{X} \) be the average of the 36 races.
**Explain or show work for all part of the question.**
A. In words, \( \overline{X} \) =
B. \( \overline{X} \sim \, \, (\, \, \, \, \, \, \, \, ) \)
C. Find the IQR for the average finishing time in these 36 races.
D. Find the probability that the runner will average in under 24 hours in these 36 races.
E. How many races should be considered if we want the standard deviation of \( \overline{X} \) to be half (1.5 hours) of the standard deviation given in the problem.
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