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 $p_{17}$, the 17th percentile. this is the bone density score separating the bottom 17% from the top 83%. which graph represents $p_{17}$? choose the correct graph below. the bone density score corresponding to $p_{17}$ is . (round to two decimal places as needed.)

Explanation:

Step1: Use z - table

We know that for a standard normal distribution $Z\sim N(0,1)$, we want to find the z - score $z$ such that $P(Z < z)=0.17$. Looking up the value 0.17 in the standard normal (z -) table.

Step2: Identify z - score

From the z - table, the z - score corresponding to a cumulative probability of 0.17 is approximately $z=-0.95$.

For the graph, the 17th percentile $P_{17}$ means that the area to the left of the value on the standard - normal curve is 0.17. The correct graph is the one where the shaded area is on the left - hand side of the curve.

Answer:

The correct graph is the one with the shaded area to the left of $P_{17}$ (usually the left - most shaded graph among the options). The bone density score corresponding to $P_{17}$ is $- 0.95$.