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. find the probability that a given score is less than - 1.06 and draw a sketch of the region. sketch the region. choose the correct graph below.

Explanation:

Step1: Use standard - normal table

We want to find $P(Z < - 1.06)$ where $Z$ is a standard - normal random variable with mean $\mu = 0$ and standard deviation $\sigma=1$. We look up the value of $-1.06$ in the standard - normal table (the $z$-table).

Step2: Read the probability

From the standard - normal table, the value corresponding to $z=-1.06$ is $0.1446$. So $P(Z < - 1.06)=0.1446$.
For the sketch, the correct graph is the one where the shaded region is to the left of $z =-1.06$ on the standard - normal curve. That is graph A.

Answer:

The probability that a given score is less than $-1.06$ is $0.1446$. The correct graph for the sketch is A.