The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.3 minutes. 17 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( 22 V. 2.3 b. What is the distribution of ? -N( 22 V, 0.5578 c. What is the distribution of x? ) x - N( 374 V, 9.4831 ) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.5633 and 21.9633 minutes. 0.0713 e. For the 17 runners, find the probability that their average time is between 21.5633 and 21.9633 minutes. .0199 f. Find the probability that the randomly selected 17 person team will have a total time more than 363.8. 0.1401 g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 15% of all 17 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
The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.3 minutes. 17 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( 22 V. 2.3 b. What is the distribution of ? -N( 22 V, 0.5578 c. What is the distribution of x? ) x - N( 374 V, 9.4831 ) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 21.5633 and 21.9633 minutes. 0.0713 e. For the 17 runners, find the probability that their average time is between 21.5633 and 21.9633 minutes. .0199 f. Find the probability that the randomly selected 17 person team will have a total time more than 363.8. 0.1401 g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 15% of all 17 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
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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Please do all parts of the question and show your work. Thanks
Transcribed Image Text:The average time to run the 5K fun run is 22 minutes and the standard deviation is 2.3 minutes. 17 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( 22
2.3
b. What is the distribution of ? - N 22
V, 0.5578
c. What is the distribution of x? ) x - N( 374
9.4831
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
21.5633 and 21.9633 minutes. 0.0713
e. For the 17 runners, find the probability that their average time is between 21.5633 and 21.9633
minutes. .0199
f. Find the probability that the randomly selected 17 person team will have a total time more than
363.8. 0.1401
g. For part e) and f), is the assumption of normal necessary? O YesO No
h. The top 15% of all 17 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:
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