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 - 1.11 and draw a sketch of the region. sketch the region. choose the correct graph below. oa. ob. oc. od.

Explanation:

Step1: Identify the distribution

The test - scores are normally distributed with mean $\mu = 0$ and standard deviation $\sigma=1$, which is a standard normal distribution $Z\sim N(0,1)$. We want to find $P(Z < - 1.11)$.

Step2: Use the standard - normal table

We look up the value of $-1.11$ in the standard - normal table (the cumulative distribution function of the standard normal distribution $\varPhi(z)$). The standard - normal table gives the cumulative probability $P(Z < z)$. Looking up $z=-1.11$ in the table, we find that $P(Z < - 1.11)=0.1335$.

Step3: Select the correct graph

The region $P(Z < - 1.11)$ is the area to the left of $z =-1.11$ under the standard - normal curve. So the correct graph is the one where the shaded region is to the left of $-1.11$ on the horizontal axis.

Answer:

The probability that a given score is less than $-1.11$ is $0.1335$. The correct graph is B (since it shows the shaded region to the left of $-1.11$ under the normal - distribution curve).