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 0.68. sketch the region. choose the correct graph below. the probability is (round to four decimal places as needed.)

Explanation:

Step1: Use the standard normal distribution

For a standard normal distribution \(Z\sim N(0,1)\), we want to find \(P(Z > 0.68)\).

Step2: Apply the property of the normal distribution

We know that \(P(Z>z)=1 - P(Z\leq z)\). Looking up the value of \(P(Z\leq0.68)\) in the standard - normal table (or using a calculator with a normal - distribution function). Using a standard - normal table or a calculator (e.g., in Excel: NORM.S.DIST(0.68, TRUE)), we find that \(P(Z\leq0.68) = 0.7517\).

Step3: Calculate the probability

Then \(P(Z > 0.68)=1 - 0.7517=0.2483\).

Answer:

\(0.2483\)