What is the distribution of X? X What is the distribution of ? - What is the distribution of

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.5 minutes. 42 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 - NG
b. What is the distribution of x? a - N(
c. What is the distribution of æ? -
N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
19.8213 and 20.1213 minutes.
e. For the 42 runners, find the probability that their average time is between 19.8213 and 20.1213
minutes.
f. Find the probability that the randomly selected 42 person team will have a total time less than
848.4.
g. For part e) and f), is the assumption of normal necessary? O NoO Yes
h. The top 20% of all 42 person team relay races will compete in the championship round. These are the
20% 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 Helpful Videos:
Transcribed Image Text:The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.5 minutes. 42 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 - NG b. What is the distribution of x? a - N( c. What is the distribution of æ? - N( d. If one randomly selected runner is timed, find the probability that this runner's time will be between 19.8213 and 20.1213 minutes. e. For the 42 runners, find the probability that their average time is between 19.8213 and 20.1213 minutes. f. Find the probability that the randomly selected 42 person team will have a total time less than 848.4. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 20% of all 42 person team relay races will compete in the championship round. These are the 20% 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 Helpful Videos:
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