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 p₁₁, the 11th percentile. this is the bone density score separating the bottom 11% from the top 89%.
which graph represents p₁₁? choose the correct graph below.
the bone density score corresponding to p₁₁ is □. (round to two decimal places as needed.)

Explanation:

Step1: Find the z - score corresponding to the 11th percentile

The 11th percentile means that \(P(X\leq x)=0.11\). Using the standard normal distribution table (or a calculator with a normal - distribution function, such as the inverse of the cumulative distribution function for the standard normal distribution \(Z\sim N(0,1)\)).
If \(P(Z\leq z)=0.11\), looking up in the standard normal table (or using a calculator: for example, in Excel, we can use the formula =NORM.S.INV(0.11)).

Step2: Calculate the z - score

Using a calculator or standard normal table, \(z\approx - 1.23\)

Answer:

\(-1.23\)