Stats: Modeling the World Nasta Edition Grades 9-12
Stats: Modeling the World Nasta Edition Grades 9-12
3rd Edition
ISBN: 9780131359581
Author: David E. Bock, Paul F. Velleman, Richard D. De Veaux
Publisher: PEARSON
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter PI, Problem 22RE

(a)

To determine

To find out what percent of the times should be within 0.5 second of 78.21 .

(a)

Expert Solution
Check Mark

Answer to Problem 22RE

  37.59% .

Explanation of Solution

In the question, it is given the table showing the top women’s skating times. Thus, we know that the mean finishing time was 78.21 seconds and the standard deviation is 1.03 seconds. Now, if the normal model is appropriate then, we have,

  78.210.5=77.7178.21+0.5=78.71z=77.7178.211.03=0.49z=78.2177.711.03=0.49

And thus the percent of the times should be within 0.5 second of 78.21 is calculated as:

  =normalcdf(0.49,0.49)=37.59%

(b)

To determine

To find out what percent of the times actually falls within this interval.

(b)

Expert Solution
Check Mark

Answer to Problem 22RE

  16% .

Explanation of Solution

In the question, it is given the table showing the top women’s skating times. Thus, we know that the mean finishing time was 78.21 seconds and the standard deviation is 1.03 seconds. Thus, we have,

  77.7178.09,78.35,78.59,78.6578.71

Therefore, the percent of the times actually falls within this interval is calculated as:

  =425=16%

(c)

To determine

To explain the discrepancy between part (a) and (b).

(c)

Expert Solution
Check Mark

Explanation of Solution

In the question, it is given the table showing the top women’s skating times. Thus, we know that the mean finishing time was 78.21 seconds and the standard deviation is 1.03 seconds. Thus, the times do not actually follow a normal model. The slower time is barely one standard deviation from the mean. Thus, that is why there is discrepancy between part (a) and (b).

Knowledge Booster
Background pattern image
Statistics
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.
Recommended textbooks for you
Text book image
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Text book image
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Text book image
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Text book image
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
Text book image
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Text book image
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License