Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation 1. Draw a graph and find P,, the 7th percentile. This is the bone density score separating the bottom 7% from the top 93%. Which graph represents P,? Choose the correct graph below. O A. OB. OD. P7 P7 P P7 The bone density score corresponding to P, is- (Round to two decimal places as needed.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Bone Density Test and Graphical Representation**
Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1.
1. **Objective**: Draw a graph and find \( P_7 \), the 7th percentile. This is the bone density score separating the bottom 7% from the top 93%.
**Which graph represents \( P_7 \)? Choose the correct graph below:**
- **Option A**:
- Description: A normal distribution curve, shaded to the left of \( P_7 \), indicating the bottom 7%.
- **Option B**:
- Description: A normal distribution curve with the left portion shaded at \( P_7 \), indicating the 7th percentile.
- **Option C**:
- Description: A normal distribution curve with shading at a different position.
- **Option D**:
- Description: A normal distribution curve with shading at a different position.
**The bone density score corresponding to \( P_7 \) is \([ \rule{1cm}{0.2pt} ]\)**
(Round to two decimal places as needed.)
**Graph Details:**
Each graph illustrates a normal distribution (bell-shaped curve) along the x-axis, and the point \( P_7 \) marks the position where the score meets the desired percentile. The correct graph will have a shaded region to indicate the portion of data below the 7th percentile.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9f85786-3779-4aaf-b559-858e5685ea13%2F84f29379-5c22-4afe-919d-43a79c226e77%2Fy31vw4v_processed.jpeg&w=3840&q=75)
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