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 p₁₀, the 10th percentile. this is the bone density score separating the bottom 10% from the top 90%. which graph represents p₁₀? choose the correct graph below. the bone density score corresponding to p₁₀ is (round to two decimal places as needed.)

Explanation:

Step1: Recall the definition of the 10th percentile

The 10th percentile ($P_{10}$) is the value such that 10% of the data lies to the left of it in a standard - normal distribution with mean $\mu = 0$ and standard deviation $\sigma=1$. The area to the left of $P_{10}$ under the standard - normal curve is $A = 0.1000$.

Step2: Use the standard - normal table (z - table)

We look up the z - score corresponding to an area of 0.1000 in the body of the standard - normal table. Looking up the closest value to 0.1000 in the standard - normal table, the z - score is approximately $z=- 1.28$.

Answer:

-1.28