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 2.35 and draw a sketch of the region. sketch the region. choose the correct graph below.

Explanation:

Step1: Identify the distribution

The test - scores are normally distributed with mean $\mu = 0$ and standard deviation $\sigma=1$, i.e., a standard normal distribution $Z\sim N(0,1)$. We want to find $P(Z < 2.35)$.

Step2: Use the standard - normal table

We look up the value of 2.35 in the standard - normal (z - table). The z - table gives the cumulative probability $P(Z < z)$ for a given z - value. Looking up 2.35 in the standard - normal table, we find that $P(Z < 2.35)=0.9906$.

Step3: Sketch the region

The standard normal curve is a bell - shaped curve centered at 0. We shade the area to the left of $z = 2.35$ under the curve. The correct graph is the one where the bell - shaped curve is centered at 0 and the area to the left of 2.35 is shaded. That is option A.

Answer:

The probability that a given score is less than 2.35 is 0.9906. The correct graph for the sketch of the region is A.