Homework Help is Here – Start Your Trial Now!
Math
Statistics
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of and a standard deviation graph and find the probability of a bone density test score less than 0. Sketch the region. Choose the correct graph below. A. O B. O C. OD. ^ A probability is nd to four decimal places as needed.)

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of and a standard deviation graph and find the probability of a bone density test score less than 0. Sketch the region. Choose the correct graph below. A. O B. O C. OD. ^ A probability is nd to four decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
### Bone Density Test Probability When examining bone density test scores, often the scores follow a normal distribution. This specific example involves scores that are distributed with a mean of 0 and a standard deviation of 1. The task is to determine the probability of a bone density test score being less than 0. To visualize this, the correct graph representation must be chosen. The graph should depict the normal distribution curve shaded to the left of the score 0 (since we are interested in the probability of scores less than 0). #### Graph Options - **Option A:** A normal distribution curve completely shaded. - **Option B:** A normal distribution curve with the left half shaded and the midpoint (0) included. - **Option C:** A normal distribution curve with only a small section to the left of 0 shaded. - **Option D:** A normal distribution curve with the right half shaded and the midpoint (0) included. Since we are focusing on scores less than 0, the correct graph is **Option B**, which shows the left section of the curve shaded from 0 onwards. #### Calculation of Probability In a standard normal distribution with a mean of 0 and a standard deviation of 1, the probability (P) of a value less than 0 is: \[ P(X < 0) = 0.5 \] This is because the mean divides the distribution into two equal halves. ### Final Answer The sketch of the region corresponding to the bone density test score less than 0 is represented correctly by **Graph B**. The probability is: \[ \text{The probability is } 0.5 \] Please round to four decimal places as needed in your specific calculations when applying similar distributions in other contexts.
Transcribed Image Text:### Bone Density Test Probability When examining bone density test scores, often the scores follow a normal distribution. This specific example involves scores that are distributed with a mean of 0 and a standard deviation of 1. The task is to determine the probability of a bone density test score being less than 0. To visualize this, the correct graph representation must be chosen. The graph should depict the normal distribution curve shaded to the left of the score 0 (since we are interested in the probability of scores less than 0). #### Graph Options - **Option A:** A normal distribution curve completely shaded. - **Option B:** A normal distribution curve with the left half shaded and the midpoint (0) included. - **Option C:** A normal distribution curve with only a small section to the left of 0 shaded. - **Option D:** A normal distribution curve with the right half shaded and the midpoint (0) included. Since we are focusing on scores less than 0, the correct graph is **Option B**, which shows the left section of the curve shaded from 0 onwards. #### Calculation of Probability In a standard normal distribution with a mean of 0 and a standard deviation of 1, the probability (P) of a value less than 0 is: \[ P(X < 0) = 0.5 \] This is because the mean divides the distribution into two equal halves. ### Final Answer The sketch of the region corresponding to the bone density test score less than 0 is represented correctly by **Graph B**. The probability is: \[ \text{The probability is } 0.5 \] Please round to four decimal places as needed in your specific calculations when applying similar distributions in other contexts.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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
SEE MORE TEXTBOOKS