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The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.6 minutes. 8 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 æ? ¤ - 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 23.7212 and 24.9212 minutes. e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212 minutes. f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4. g. For part e) and f), is the assumption of normal necessary? C NoO Yes h. The top 15% of all 8 person team relay races will compete in the championship round. These are the 15% 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 24 minutes and the standard deviation is 2.6 minutes. 8 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 æ? ¤ - 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 23.7212 and 24.9212 minutes. e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212 minutes. f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4. g. For part e) and f), is the assumption of normal necessary? C NoO Yes h. The top 15% of all 8 person team relay races will compete in the championship round. These are the 15% 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
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 24 minutes and the standard deviation is 2.6 minutes. 8 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 ? ¤ - N( Σε Στ- 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 23.7212 and 24.9212 minutes. e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212 minutes. f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 15% of all 8 person team relay races will compete in the championship round. These are the 15% 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 24 minutes and the standard deviation is 2.6 minutes. 8 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 ? ¤ - N( Σε Στ- 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 23.7212 and 24.9212 minutes. e. For the 8 runners, find the probability that their average time is between 23.7212 and 24.9212 minutes. f. Find the probability that the randomly selected 8 person team will have a total time less than 186.4. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 15% of all 8 person team relay races will compete in the championship round. These are the 15% 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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