Question

assume that a randomly selected subject is given a bone density test. bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. draw a graph and find (p_{8}), the 8th percentile. this is the bone density score separating the bottom 8% from the top 92%. which graph represents (p_{8})? choose the correct graph below. a. b. c. d. the bone density score corresponding to (p_{8}) is. (round to two decimal places as needed.)

Explanation:

Step1: Use z - score table

We know that we want to find the z - score corresponding to the 8th percentile. Looking up the value 0.08 in the standard normal distribution table (z - table), we find the z - score.

Step2: Identify z - score

From the standard normal table, the z - score corresponding to an area of 0.08 to the left of it is approximately - 1.41.

Answer:

The correct graph is the one where the area to the left of $P_8$ is shaded and represents 8% of the total area under the curve (usually the left - most shaded graph among the options). The bone density score corresponding to $P_8$ is - 1.41.