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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( 24 2.6 b. What is the distribution of æ? ¤ - N( 24 0.9192 v) đ c. What is the distribution of > x? ) x - N( 192 d. If one randomly selected runner is timed, find the probability that this runner's time will be between V, 7.3539 v) o 192 o 7.3539 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

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( 24 2.6 b. What is the distribution of æ? ¤ - N( 24 0.9192 v) đ c. What is the distribution of > x? ) x - N( 192 d. If one randomly selected runner is timed, find the probability that this runner's time will be between V, 7.3539 v) o 192 o 7.3539 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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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( 24 2.6 b. What is the distribution of ? ī - N( 24 0.9192 c. What is the distribution of > x? > x - N( 192 7.3539 v) 192 o 7.3539 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( 24 2.6 b. What is the distribution of ? ī - N( 24 0.9192 c. What is the distribution of > x? > x - N( 192 7.3539 v) 192 o 7.3539 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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