The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 minutes. 43 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 a? - N( c. What is the distribution of a? - N d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.7824 and 22.2824 minutes. e. For the 43 runners, find the probability that their average time is between 21.7824 and 22.2824 minutes. f. Find the probability that the randomly selected 43 person team will have a total time less than 967.5. g. For part e) and f), is the assumption of normal necessary? O No Yes h. The top 15% of all 43 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 minutes championship round? Hint: Some Helpful Videos: • Finding the Sampling Distribution [+] • Finding a Probability Using the Central Limit Theorem [+] • Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums [+]
The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 minutes. 43 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 a? - N( c. What is the distribution of a? - N d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.7824 and 22.2824 minutes. e. For the 43 runners, find the probability that their average time is between 21.7824 and 22.2824 minutes. f. Find the probability that the randomly selected 43 person team will have a total time less than 967.5. g. For part e) and f), is the assumption of normal necessary? O No Yes h. The top 15% of all 43 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 minutes championship round? Hint: Some Helpful Videos: • Finding the Sampling Distribution [+] • Finding a Probability Using the Central Limit Theorem [+] • Finding Value Given a Probability Using the Central Limit Theorem [+] • The Central Limit Theorem For Sums [+]
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 minutes. 43 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 a? a- N(
c. What is the distribution of ) x? x - N(
С.
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7824 and 22.2824 minutes.
e. For the 43 runners, find the probability that their average time is between 21.7824 and 22.2824
minutes.
f. Find the probability that the randomly selected 43 person team will have a total time less than 967.5.
g. For part e) and f), is the assumption of normal necessary? ONo Yes
h. The top 15% of all 43 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
Hint:
Some Helpful Videos:
• Finding the Sampling Distribution [+]
• Finding a Probability Using the Central Limit Theorem [+]
Finding Value Given a Probability Using the Central Limit Theorem [+]
• The Central Limit Theorem For Sums [+]
Hint
RasmusseRC
habits-g ged)pglf 7-
mussen
FAGES
18,538
1.
W
DEC
átv
8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24b8115f-9a19-47b6-814b-3be924127cef%2Fc403d236-a4d9-4030-948e-568a85530268%2Fpcgn0l8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.7 minutes. 43 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 a? a- N(
c. What is the distribution of ) x? x - N(
С.
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.7824 and 22.2824 minutes.
e. For the 43 runners, find the probability that their average time is between 21.7824 and 22.2824
minutes.
f. Find the probability that the randomly selected 43 person team will have a total time less than 967.5.
g. For part e) and f), is the assumption of normal necessary? ONo Yes
h. The top 15% of all 43 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
Hint:
Some Helpful Videos:
• Finding the Sampling Distribution [+]
• Finding a Probability Using the Central Limit Theorem [+]
Finding Value Given a Probability Using the Central Limit Theorem [+]
• The Central Limit Theorem For Sums [+]
Hint
RasmusseRC
habits-g ged)pglf 7-
mussen
FAGES
18,538
1.
W
DEC
átv
8.
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