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 2.09 and draw a sketch of the region.
sketch the region. choose the correct graph below.
the probability is
(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 z - table gives the cumulative probability $P(Z < z)$ for a given z - value. Looking up $z = 2.09$ in the standard - normal table, we find that the value corresponding to 2.09 is 0.9817.

Answer:

0.9817