Question

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

Explanation:

Step1: Recall percentile definition

The $3$rd percentile $P_3$ is the value such that $3\%$ of the data lies to the left of it in a normal - distribution.

Step2: Analyze normal - distribution graph

In a standard normal distribution with mean $\mu = 0$ and standard deviation $\sigma=1$, the left - hand side of the distribution represents the lower values. The shaded area to the left of $P_3$ should be $3\%$ of the total area under the curve.

Answer:

A. The graph with the shaded area to the left of $P_3$ representing $3\%$ of the total area under the normal - distribution curve.