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.)
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.3: Shapes Of Distributions
Problem 8Q
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa058bb5e-e178-4408-8d52-426bc36636a3%2Fd19cdca3-6191-42f8-8397-795c1cd21731%2Ftpmmatm_processed.jpeg&w=3840&q=75)
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.
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