113 7.7 Topic 7: The Normal Distribution 00. Suppose a population is unimodal and symmetric with mean 55 and standard deviation 7. Use Figure 7.11 to aid in answering the following questions. (a) Approximately what percent of observations are below 34? (b) Approximately what percent of observations are above 55? (c) Approximately what percent of observations are between 41 and 62? (d) Approximately what percent of observations are above 48? Figure 7.11: Depiction of the Empirical Rule for X N(55, 7) X: 34 41 48 55 62 69 76 Z: -3 -2 -1 2 57. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The area below z = 1.3. (b) The area below z =-1.3. (c) The area above z = 1.3. %3D (d) The area between z = -1.3 and z = 1.3. 58. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What is the probability that the average person has a time faster than Usain Bolt's record of 9.58 seconds? 59. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The z-score of the 45th percentile. 60. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What speed is the third quartile? Hint: The third quartile represents what percentile? (b) The z-score for the top 20%. 3.

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
Topic Video
Question

Question 56 parts A and B

113
7.7
Topic 7: The Normal Distribution
00. Suppose a population is unimodal and symmetric with mean 55 and standard deviation 7. Use
Figure 7.11 to aid in answering the following questions.
(a) Approximately what percent of observations are below 34?
(b) Approximately what percent of observations are above 55?
(c) Approximately what percent of observations are between 41 and 62?
(d) Approximately what percent of observations are above 48?
Figure 7.11: Depiction of the Empirical Rule for X N(55, 7)
X: 34
41
48
55
62
69
76
Z: -3
-2
-1
2
57. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator.
(a) The area below z = 1.3.
(b) The area below z =-1.3.
(c) The area above z = 1.3.
%3D
(d) The area between z = -1.3 and z = 1.3.
58. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean
14 seconds and standard deviation 0.8 seconds. What is the probability that the average person
has a time faster than Usain Bolt's record of 9.58 seconds?
59. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator.
(a) The z-score of the 45th percentile.
60. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean
14 seconds and standard deviation 0.8 seconds. What speed is the third quartile? Hint: The
third quartile represents what percentile?
(b) The z-score for the top 20%.
3.
Transcribed Image Text:113 7.7 Topic 7: The Normal Distribution 00. Suppose a population is unimodal and symmetric with mean 55 and standard deviation 7. Use Figure 7.11 to aid in answering the following questions. (a) Approximately what percent of observations are below 34? (b) Approximately what percent of observations are above 55? (c) Approximately what percent of observations are between 41 and 62? (d) Approximately what percent of observations are above 48? Figure 7.11: Depiction of the Empirical Rule for X N(55, 7) X: 34 41 48 55 62 69 76 Z: -3 -2 -1 2 57. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The area below z = 1.3. (b) The area below z =-1.3. (c) The area above z = 1.3. %3D (d) The area between z = -1.3 and z = 1.3. 58. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What is the probability that the average person has a time faster than Usain Bolt's record of 9.58 seconds? 59. Consider the standard normal distribution, Z ~ N(0, 1). Find the following using the calculator. (a) The z-score of the 45th percentile. 60. Suppose times for the 100m sprint for the average person are unimodal and symmetric with mean 14 seconds and standard deviation 0.8 seconds. What speed is the third quartile? Hint: The third quartile represents what percentile? (b) The z-score for the top 20%. 3.
Expert Solution
Step 1

According to the provided information,

Statistics homework question answer, step 1, image 1

a)

The percentage of observation is below 34 can be calculated as:

Statistics homework question answer, step 1, image 2

Therefore, 0.13% of the observation is below 34.

steps

Step by step

Solved in 2 steps with 3 images

Blurred answer
Knowledge Booster
Permutation and Combination
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
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