The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.7 minutes. 40 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.If one randomly selected runner is timed, find the probability that this runner's time will be between 23.8596 and 24.1596 minutes.For the 40 runners, find the probability that their average time is between 23.8596 and 24.1596 minutes.Find the probability that the randomly selected 40 person team will have a total time less than 944.For part e) and f), is the assumption of normal necessary? NoYesThe top 15% of all 40 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

As per Bartleby guideline expert have to answer first question three subparts only dear student…

Answered: The average time to run the 5K fun run…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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The average time to run the 5K fun run is 24 minutes and the standard deviation is 2.7 minutes. 40 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

If one randomly selected runner is timed, find the probability that this runner's time will be between 23.8596 and 24.1596 minutes.
For the 40 runners, find the probability that their average time is between 23.8596 and 24.1596 minutes.
Find the probability that the randomly selected 40 person team will have a total time less than 944.
For part e) and f), is the assumption of normal necessary? NoYes
The top 15% of all 40 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

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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