The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.6 minutes. 14 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( 25 2.6 b. What is the distribution of a? ¤ - N( 25 .6949 c. What is the distribution of ) x? ) N( 350 9.7283 ) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 25.1576 and 25.9576 minutes. .1195 e. For the 14 runners, find the probability that their average time is between 25.1576 and 25.9576 minutes. .3262

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.6 minutes. 14 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( 25
2.6
b. What is the distribution of a? ¤ - N( 25
.6949
c. What is the distribution of ) x? )
N( 350
9.7283 ) o
d. If one randomly selected runner is timed, find the probability that this runner's time will be between
25.1576 and 25.9576 minutes. .1195
e. For the 14 runners, find the probability that their average time is between 25.1576 and 25.9576
minutes. .3262
Transcribed Image Text:The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.6 minutes. 14 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( 25 2.6 b. What is the distribution of a? ¤ - N( 25 .6949 c. What is the distribution of ) x? ) N( 350 9.7283 ) o d. If one randomly selected runner is timed, find the probability that this runner's time will be between 25.1576 and 25.9576 minutes. .1195 e. For the 14 runners, find the probability that their average time is between 25.1576 and 25.9576 minutes. .3262
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Continuous Probability Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman