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 0.97. sketch the region. choose the correct graph below.

Explanation:

Step1: Recall the standard - normal distribution property

Let \(Z\) be a standard - normal random variable with mean \(\mu = 0\) and standard deviation \(\sigma=1\). We want to find \(P(Z > 0.97)\).

Step2: Use the property of the total area under the curve

The total area under the standard - normal curve is 1, and \(P(Z>z)=1 - P(Z\leq z)\).
We know from the standard - normal table (or z - table), \(P(Z\leq0.97)\) can be looked up. From the z - table, \(P(Z\leq0.97) = 0.8340\).

Step3: Calculate the probability

\(P(Z > 0.97)=1 - P(Z\leq0.97)=1 - 0.8340 = 0.1660\).
For the graph, we are looking for the area to the right of \(z = 0.97\) under the standard - normal curve. The correct graph is C since it shows the shaded region to the right of \(z = 0.97\).

Answer:

The probability is \(0.1660\) and the correct graph is C.