**Problem Statement:**3. Walter usually meets Julia at the track. He prefers to jog 3 miles. From long experience, he knows that the standard deviation for his jogging times is 2.40 minutes. For a random sample of 90 jogging sessions, the mean time was 22.5 minutes. Find a 99% confidence interval for the mean jogging time for all of Walter's 3-mile running times over the past several years.**Solution Approach:**To calculate the 99% confidence interval for the mean jogging time, use the following formula for the confidence interval of the mean:\[ \text{Confidence Interval} = \bar{x} \pm z \left(\frac{\sigma}{\sqrt{n}}\right) \]Where:- $\bar{x}$ is the sample mean (22.5 minutes).- $z$ is the z-score corresponding to the confidence level (99%). For 99%, $z \approx 2.576$.- $\sigma$ is the population standard deviation (2.40 minutes).- $n$ is the sample size (90).**Steps:**1. Calculate the standard error (SE): \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{2.40}{\sqrt{90}} \]2. Multiply the standard error by the z-score: \[ ME = 2.576 \times SE \] (ME is the margin of error)3. Determine the confidence interval: \[ \text{Lower limit} = \bar{x} - ME \] \[ \text{Upper limit} = \bar{x} + ME \]These steps will provide the 99% confidence interval for the mean jogging time for all of Walter's 3-mile runs over the past several years.

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Description: **Problem Statement:**3. Walter usually meets Julia at the track. He prefers to jog 3 miles. From long experience, he knows that the standard deviation for his jogging times is 2.40 minutes. For a random sample of 90 jogging sessions, the mean time

Answer : The given values are mean=x=2.25 population variance = σ =2.40 sample size = n =90

Math

Statistics

3. Walter usually meets Julia at the track. He prefers to jog 3 miles. From long experience, he knows that the standard deviation for his jogging times is 2.40 minutes. For a random sample of 90 jogging sessions, the mean time was 2.25 minutes. Find a 99% confidence interval for the mean jogging time for all of Walter's 3-mile running times over the past several years.

3. Walter usually meets Julia at the track. He prefers to jog 3 miles. From long experience, he knows that the standard deviation for his jogging times is 2.40 minutes. For a random sample of 90 jogging sessions, the mean time was 2.25 minutes. Find a 99% confidence interval for the mean jogging time for all of Walter's 3-mile running times over the past several years.

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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