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 0.38. sketch the region. choose the correct graph below. a. graph with shaded region to the right of 0.38 b. graph with shaded region between - 0.38 and 0.38 c. graph with shaded region to the left of 0.38 d. graph with shaded region to the left of - 0.38 the probability is . (round to four decimal places as needed.)

Explanation:

Step1: Recall the standard - normal distribution property

We know that if \(Z\) is a standard - normal random variable (\(Z\sim N(0,1)\)), and we want to find \(P(Z > 0.38)\). The total area under the standard - normal curve is 1, and \(P(Z>z)=1 - P(Z\leq z)\).

Step2: Use the standard - normal table

We look up the value of \(P(Z\leq0.38)\) in the standard - normal table (z - table). From the z - table, \(P(Z\leq0.38) = 0.6480\).

Step3: Calculate the required probability

\(P(Z > 0.38)=1 - P(Z\leq0.38)=1 - 0.6480 = 0.3520\)

For the graph, we are looking for the area to the right of \(z = 0.38\) under the standard - normal curve. The correct graph is the one where the shaded region is to the right of \(z = 0.38\), which is option A.

Answer:

A. (The graph with the shaded region to the right of \(z = 0.38\))
0.3520