Question

assume that a randomly - selected subject is given a bone density test. these 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 2.09 and draw a sketch of the region. sketch the region. choose the correct graph below. a. b. c. d. the probability is 0.9817 (round to four decimal places as needed).

Explanation:

Step1: Recall standard - normal distribution

We have a standard normal distribution $Z\sim N(0,1)$. We want to find $P(Z < 2.09)$.

Step2: Use the standard - normal table

We look up the value of 2.09 in the standard - normal (z - table). The table gives the cumulative probability from $-\infty$ to the z - score. Looking up 2.09 in the z - table, we find that the cumulative probability $P(Z < 2.09)=0.9817$.

Answer:

The probability is 0.9817. The correct graph is the one that has the area under the standard - normal curve shaded to the left of 2.09 (which is option D assuming option D is the one with the left - hand side of 2.09 shaded).