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 - 1.52. sketch the region. choose the correct graph below. oa. -1.52 ob. 1.52 oc. -1.52 od. -1.52 1.52

Explanation:

Step1: Analyze the z - score

We are looking for the probability that \(z>- 1.52\). The standard normal distribution is symmetric about \(z = 0\). The total area under the standard normal curve is \(1\).

Step2: Use the property of the standard normal distribution

The area to the left of \(z=-1.52\) can be found using the standard normal table. Let \(P(Z < - 1.52)\) be the area to the left of \(z=-1.52\). Then \(P(Z>-1.52)=1 - P(Z < - 1.52)\).
From the standard - normal table, \(P(Z < - 1.52)=0.0643\). So \(P(Z>-1.52)=1 - 0.0643=0.9357\).

Step3: Sketch the region

The region for \(P(Z > - 1.52)\) is the area to the right of \(z=-1.52\) under the standard normal curve.

Answer:

C.