The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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 b. What is the distribution of I? ~ N( c. What is the distribution of Σa? - N
The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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 b. What is the distribution of I? ~ N( c. What is the distribution of Σa? - N
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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Question
need help with this, please!
![The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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-NO
b. What is the distribution of ? ~ N(
c. What is the distribution of Σ? Σ ~ N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7741 and 22.4741 minutes.
e. For the 12 runners, find the probability that their average time is between 21.7741 and 22.4741
minutes.
f. Find the probability that the randomly selected 12 person team will have a total time less than
261.6.
g. For part e) and f), is the assumption of normal necessary? O No Yes
h. The top 15% of all 12 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc260e632-e4e2-45c7-853f-2d07e95220d0%2F735975f0-242a-4860-91ab-ef881b489df0%2Fmm0dfo7_processed.png&w=3840&q=75)
Transcribed Image Text:The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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-NO
b. What is the distribution of ? ~ N(
c. What is the distribution of Σ? Σ ~ N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7741 and 22.4741 minutes.
e. For the 12 runners, find the probability that their average time is between 21.7741 and 22.4741
minutes.
f. Find the probability that the randomly selected 12 person team will have a total time less than
261.6.
g. For part e) and f), is the assumption of normal necessary? O No Yes
h. The top 15% of all 12 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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Need help with parts D, E F please
![The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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-NO
b. What is the distribution of ? ~ N(
c. What is the distribution of Σ? Σ ~ N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7741 and 22.4741 minutes.
e. For the 12 runners, find the probability that their average time is between 21.7741 and 22.4741
minutes.
f. Find the probability that the randomly selected 12 person team will have a total time less than
261.6.
g. For part e) and f), is the assumption of normal necessary? O No Yes
h. The top 15% of all 12 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](https://content.bartleby.com/qna-images/question/c260e632-e4e2-45c7-853f-2d07e95220d0/40d7c20e-8c28-47ff-8e51-fb1b6b50f9e9/bqdsbr_thumbnail.png)
Transcribed Image Text:The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.6 minutes. 12 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-NO
b. What is the distribution of ? ~ N(
c. What is the distribution of Σ? Σ ~ N(
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7741 and 22.4741 minutes.
e. For the 12 runners, find the probability that their average time is between 21.7741 and 22.4741
minutes.
f. Find the probability that the randomly selected 12 person team will have a total time less than
261.6.
g. For part e) and f), is the assumption of normal necessary? O No Yes
h. The top 15% of all 12 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
Solution
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