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 - 1.88. sketch the region. choose the correct graph below.

Explanation:

Step1: Recall the standard - normal distribution property

We know that for a standard - normal distribution \(Z\sim N(0,1)\), and we want to find \(P(Z > - 1.88)\).

Step2: Use the symmetry of the standard - normal distribution

The total area under the standard - normal curve is 1. Also, \(P(Z > - 1.88)=1 - P(Z\leq - 1.88)\).

Step3: Look up the value in the standard - normal table

From the standard - normal table (z - table), \(P(Z\leq - 1.88)=0.0301\).

Step4: Calculate the probability

\(P(Z > - 1.88)=1 - 0.0301 = 0.9699\).

The correct graph is the one that has the area to the right of \(z=-1.88\) shaded. So the graph with the area to the right of \(z = - 1.88\) shaded is the correct one.

Answer:

The probability is \(0.9699\). The correct graph is the one where the area to the right of \(z=-1.88\) on the standard - normal curve is shaded (option D if the graph with the right - hand side of \(z = - 1.88\) shaded is labeled as D).