The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 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.What is the distribution of X? X ~ N(,)What is the distribution of ¯x¯? ¯x¯ ~ N(,)What is the distribution of ∑x? ∑x ~ N(,)If one randomly selected runner is timed, find the probability that this runner's time will be between 20.8833 and 21.4833 minutes. For the 40 runners, find the probability that their average time is between 20.8833 and 21.4833 minutes. Find the probability that the randomly selected 40 person team will have a total time less than 832. For part e) and f), is the assumption of normal necessary? YesNoThe 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

As per our guidelines we are suppose to answer three sub parts. Given ,mean (μ)=21standard deviation…

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

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 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.

What is the distribution of X? X ~ N(,)
What is the distribution of ¯x¯? ¯x¯ ~ N(,)
What is the distribution of ∑x? ∑x ~ N(,)
If one randomly selected runner is timed, find the probability that this runner's time will be between 20.8833 and 21.4833 minutes.
For the 40 runners, find the probability that their average time is between 20.8833 and 21.4833 minutes.
Find the probability that the randomly selected 40 person team will have a total time less than 832.
For part e) and f), is the assumption of normal necessary? YesNo
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

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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