Questions: 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. Draw a graph and find P3, the 3rd percentile. This is the bone density score separating the bottom 3% from the top 97%. Which graph represents P3? Choose the correct graph below. A. B. C. D. The bone density score corresponding to P3 is (Round to two decimal places as needed.)

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. Draw a graph and find P3, the 3rd percentile. This is the bone density score separating the bottom 3% from the top 97%. Which graph represents P3? Choose the correct graph below. A. B. C. D. The bone density score corresponding to P3 is (Round to two decimal places as needed.)
Transcript text: 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 . Draw a graph and find $\mathrm{P}_{3}$, the 3rd percentile. This is the bone density score separating the bottom $3 \%$ from the top $97 \%$. Which graph represents $\mathrm{P}_{3}$ ? Choose the correct graph below. A. B. C. D. The bone density score corresponding to $P_{3}$ is $\square$ (Round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Understand the Problem

The problem states that bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. We need to find the bone density score corresponding to the 3rd percentile (P3), which separates the bottom 3% from the top 97%.

Step 2: Identify the Z-Score for the 3rd Percentile

In a standard normal distribution, the Z-score corresponding to the 3rd percentile can be found using a Z-table or statistical software. The Z-score for the 3rd percentile is approximately -1.88.

Step 3: Match the Graph to the Z-Score

The correct graph should show the area to the left of the Z-score -1.88 shaded, representing the bottom 3% of the distribution.

Final Answer

The correct graph is C. The bone density score corresponding to P3 is approximately -1.88.

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