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The average time to run the SK fun run is 24 minutes and the standard deviation is 2.2 minutes. 40 unners 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( c. What is the distribution of z ~ N( z? d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5781 and 23.9781 minutes. e. For the 40 runners, find the probability that their average time is between 23.5781 and 23.9781 minutes. f Find the probability that the randomly selected 40 person team will have a total time more than 964. g For part e) and f), is the assumption of normal necessary? ONo O Yes h. The top 10%% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Hint: Some Helnful Vidoor

The average time to run the SK fun run is 24 minutes and the standard deviation is 2.2 minutes. 40 unners 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( c. What is the distribution of z ~ N( z? d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5781 and 23.9781 minutes. e. For the 40 runners, find the probability that their average time is between 23.5781 and 23.9781 minutes. f Find the probability that the randomly selected 40 person team will have a total time more than 964. g For part e) and f), is the assumption of normal necessary? ONo O Yes h. The top 10%% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Hint: Some Helnful Vidoor

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 SK fun run is 24 minutes and the standard deviation is 2.2 minutes. 40 unners 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( c. What is the distribution of z ~ N( z? d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5781 and 23.9781 minutes. e. For the 40 runners, find the probability that their average time is between 23.5781 and 23.9781 minutes. f Find the probability that the randomly selected 40 person team will have a total time more than 964. g For part e) and f), is the assumption of normal necessary? ONo O Yes h. The top 10%% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Hint: Some Helnful Vidoor
Transcribed Image Text:The average time to run the SK fun run is 24 minutes and the standard deviation is 2.2 minutes. 40 unners 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( c. What is the distribution of z ~ N( z? d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.5781 and 23.9781 minutes. e. For the 40 runners, find the probability that their average time is between 23.5781 and 23.9781 minutes. f Find the probability that the randomly selected 40 person team will have a total time more than 964. g For part e) and f), is the assumption of normal necessary? ONo O Yes h. The top 10%% of all 40 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes Hint: Some Helnful Vidoor
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