### 5K Fun Run Time Analysis#### BackgroundThe average time to complete a 5K fun run is 22 minutes, with a standard deviation of 2.6 minutes. We are analyzing the run times of 50 randomly selected runners. Assume a normal distribution and round all answers to 4 decimal places.#### Questions and Answers**a. What is the distribution of \( X \)?**\( X \sim N(22, 2.6) \)Explanation: - \( X \) denotes the time taken by an individual runner.- Follows a normal distribution with a mean (\( \mu \)) of 22 minutes and a standard deviation (\( \sigma \)) of 2.6 minutes.**b. What is the distribution of \( \bar{x} \)?**\( \bar{x} \sim N(22, 0.3677) \)Explanation:- \( \bar{x} \) is the sample mean of the 50 runners.- The standard error of the mean is calculated as \( \frac{\sigma}{\sqrt{n}} = \frac{2.6}{\sqrt{50}} \approx 0.3677 \).**c. What is the distribution of \( \sum x \)?**\( \sum x \sim N(1100, 18.384) \)Explanation:- \( \sum x \) is the sum of the times of the 50 runners.- The mean of \( \sum x \) is \( n \times \mu = 50 \times 22 = 1100 \).- The standard deviation of \( \sum x \) is \( \sqrt{n} \times \sigma = \sqrt{50} \times 2.6 \approx 18.384 \).**d. If one randomly selected runner is timed, what is the probability that this runner's time will be between 21.9484 and 22.3484 minutes?**\[ P(21.9484 < X < 22.3484) = 0.0612 \]Explanation:- The probability is calculated using the cumulative distribution function (CDF) of the normal distribution given the specified interval.**e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484 minutes.**\[ P(21.9484

Note: Hey, since there are multiple sub-parts posted, we will answer first three parts if you want…

The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 50 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 22 2.6 b. What is the distribution of x? ¤ - N( 22 .3677 v) o Σ c. What is the distribution of ) x? > a x - N( 1100 18.384 v) o o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.9484 and 22.3484 minutes. .0612 e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484 minutes. .3841 f. Find the probability that the randomly selected 50 person team will have a total time less than 1070. .0514 g. For part e) and f), is the assumption of normal necessary? O NoO Yes o h. The top 20% of all 50 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 50 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N( 22 2.6 b. What is the distribution of x? ¤ - N( 22 .3677 v) o Σ c. What is the distribution of ) x? > a x - N( 1100 18.384 v) o o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.9484 and 22.3484 minutes. .0612 e. For the 50 runners, find the probability that their average time is between 21.9484 and 22.3484 minutes. .3841 f. Find the probability that the randomly selected 50 person team will have a total time less than 1070. .0514 g. For part e) and f), is the assumption of normal necessary? O NoO Yes o h. The top 20% of all 50 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

need help please, thank you!
Only parts b, c, and d
The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.7 minutes. 16 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X N( b. What is the distribution of a? ¤ - N( c. What is the distribution of) x? ) x - N( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.1875 and 23.9875 minutes.
Normal Distribution: 2. You have a Normal distribution with Mean= 54 and Standard Deviation 7. %3D A. Label the axis for this normal distribution. B. 95% of the data falls between and C. What is the probability of getting a value between 45 and 62? Show work. D. What is the probability of getting a value above 58? Show work. E. What observation cuts off the top 10% of the data? Show work. 3. The length of time it takes for a manufacturer to build a car is normally distributed with a mean of 20 hours and a standard deviation of 1.5 hours. Use this information to answer the following questions. A. What percent of cars are made in less than 17 hours? Show work.
I need help with b and c
Please part: d , e , f, g and h. Thanks
The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.4 minutes. 6 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X - N(d b. What is the distribution of a? a - N( c. What is the distribution of x? > x - N( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 24.9303 and 26.1303 minutes. e. For the 6 runners, find the probability that their average time is between 24.9303 and 26.1303 minutes. f. Find the probability that the randomly selected 6 person team will have a total time less than 141. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 20% of all 6 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship…
The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.4 minutes. 41 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X- N( b. What is the distribution of a? - N( c. What is the distribution of æ? x - N( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 19.5378 and 20.0378 minutes. e. For the 41 runners, find the probability that their average time is between 19.5378 and 20.0378 minutes. f. Find the probability that the randomly selected 41 person team will have a total time more than 795.4. g. For part e) and f), is the assumption of normal necessary? O No Yes h. The top 20% of all 41 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship…
Part d, e and f
I need 3 answers i will give 10 upvotes
I have answered most of the questions. Please helped me with the last 2 question G and H. Thank you
Only D & E