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 - 1.73. sketch the region. choose the correct graph below. a. b. c. d. the probability is (round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution property

For a standard normal distribution \(Z\sim N(0,1)\), the probability \(P(Z > - 1.73)\) can be found using the property \(P(Z>z)=1 - P(Z\leq z)\).

Step2: Look up the \(z -\)value in the standard - normal table

From the standard - normal table (or using a calculator with a normal - distribution function), \(P(Z\leq - 1.73)\) is the value corresponding to \(z=-1.73\). Looking up in the table: \(P(Z\leq - 1.73)=0.0418\).

Step3: Calculate \(P(Z > - 1.73)\)

Using the formula \(P(Z > - 1.73)=1 - P(Z\leq - 1.73)\). Substitute \(P(Z\leq - 1.73) = 0.0418\) into the formula: \(P(Z > - 1.73)=1-0.0418 = 0.9582\).

Answer:

\(0.9582\)