### Understanding Variability in Cross-Country Running SplitsIn college, talented runners may join a cross-country team. Runners tend to run their best times when they run even splits. Even splits occur when the runners maintain an even pace throughout the race.The cross-country coach wants to estimate the typical variability in his best runner's 1-mile splits. He takes a random sample of 25 of this runner's mile splits and finds that this runner's mean 1-mile split is 5.44 minutes per mile, with a standard deviation of 0.14 minutes per mile. This runner's 1-mile splits follow a normal distribution.#### Task (a):Find the chi-square critical values \( \chi_L^2 \) and \( \chi_U^2 \) to be used in constructing a 95% confidence interval for the true population standard deviation. (Round your answers to two decimal places.)\[ \chi_L^2 = \_\_\_\_\_\_ \]\[ \chi_U^2 = \_\_\_\_\_\_ \]#### Task (b):Find the 95% confidence interval for the true variability in his best runner's 1-mile splits. (Round your answers to three decimal places.)- Lower bound: \_\_\_\_\_\_- Upper bound: \_\_\_\_\_\_This problem involves understanding the role of variability and standard deviation in measuring performance consistency. By analyzing the data through chi-square critical values and confidence intervals, we can make informed estimates about true performance variability.

It is given that Mean = 5.44Standard deviation = 0.14Sample size = 25Confidence level = 95%

Answered: (a) Find the chi-square critical values…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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