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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( 25 2.4 b. What is the distribution of æ? ¤ - N( 25 0.9798 c. What is the distribution of ) x? > x - N( 150 V 14.4 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.

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( 25 2.4 b. What is the distribution of æ? ¤ - N( 25 0.9798 c. What is the distribution of ) x? > x - N( 150 V 14.4 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.

MATLAB: An Introduction with Applications
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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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( 25 2.4 b. What is the distribution of ? - N( 25 0.9798 c. What is the distribution of > æ? > x - N( 150 14.4 x) o 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 round? minutes
Transcribed Image Text: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( 25 2.4 b. What is the distribution of ? - N( 25 0.9798 c. What is the distribution of > æ? > x - N( 150 14.4 x) o 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 round? minutes
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