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 P12, the 12th percentile. This is the bone density score separating the bottom 12% from the top 88% Which graph represents P12? Choose the correct graph below.

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 P12, the 12th percentile. This is the bone density score separating the bottom 12% from the top 88% Which graph represents P12? Choose the correct graph below.
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 $\mathrm{P}_{12}$, the 12th percentile. This is the bone density score separating the bottom $12 \%$ from the top $88 \%$ Which graph represents $\mathrm{P}_{12}$ ? Choose the correct graph below.
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Solution

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Solution Steps

Step 1: Understand the Problem

The problem involves identifying the correct graph that represents the bone density score corresponding to the 12th percentile (P12) in a normal distribution with a mean of 0 and a standard deviation of 1.

Step 2: Identify the Characteristics of a Normal Distribution

A normal distribution is symmetric around the mean (0 in this case) and has a bell-shaped curve. Percentiles indicate the relative standing of a value within the distribution.

Step 3: Determine the Position of the 12th Percentile

The 12th percentile (P12) is the value below which 12% of the data falls. In a standard normal distribution, this value is negative because it is below the mean (0).

Step 4: Match the Graph to the 12th Percentile

Among the given options, the graph that shows a value to the left of the mean (0) represents the 12th percentile. This is because the 12th percentile is less than the mean in a standard normal distribution.

Final Answer

The correct graph representing P12 is Option A.

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