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 - 1.59. sketch the region. choose the correct graph below. oa. ob. oc. od.

Explanation:

Step1: Recall the properties of standard normal distribution

We know that if \(Z\) is a standard - normal random variable (\(\mu = 0,\sigma = 1\)), and we want to find \(P(Z>-1.59)\).

Step2: Use the property \(P(Z > z)=1 - P(Z\leq z)\)

For a standard - normal distribution, we can look up the value of \(P(Z\leq - 1.59)\) in the standard - normal table. The value of \(P(Z\leq - 1.59)\) from the standard - normal table is \(0.0559\). Then \(P(Z>-1.59)=1 - P(Z\leq - 1.59)=1 - 0.0559 = 0.9441\).
For the graph, we are looking for the area to the right of \(z=-1.59\) under the standard - normal curve. The correct graph is the one where the shaded region is to the right of \(z =-1.59\), which is option D.

Answer:

The probability is \(0.9441\) and the correct graph is D.