Question

assume that a randomly selected subject is given a bone density test. those test scores are normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find the probability of a bone density test score greater than 0.86. sketch the region. choose the correct graph below.

Explanation:

Step1: Recall the properties of the standard - normal distribution

The standard - normal distribution has a mean $\mu = 0$ and a standard deviation $\sigma=1$. We want to find $P(Z > 0.86)$, where $Z$ is a standard - normal random variable.

Step2: Use the standard - normal table

The standard - normal table (z - table) gives the cumulative probability $P(Z\leq z)$. Since the total area under the standard - normal curve is 1, we know that $P(Z > 0.86)=1 - P(Z\leq0.86)$.
Looking up $z = 0.86$ in the standard - normal table, we find that $P(Z\leq0.86)=0.8051$.

Step3: Calculate the probability

$P(Z > 0.86)=1 - 0.8051 = 0.1949$.

The correct graph is the one that has the shaded region to the right of $z = 0.86$. So the correct graph is D.

Answer:

D. The probability of a bone density test score greater than 0.86 is 0.1949.