Question

13. A doctor measured serum HDL levels in her patients, and found that they were normally distributed with a mean of 67.9 and a standard deviation of 3. Find the serum HDL levels that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.(a) z = -1.2(b) z = 1.36

Answer 1

Given:

Mean, μ = 67.9

Standard deviation, σ = 3

Let's find the HDL levels that correspond to the following z-scores.

(a) z = -1.2

To find the HDL levels, apply the z-score formula:

`z=(x-\mu)/(\sigma)`

Here, we are to solve for x.

Rewrite the formula for x.

`x=(z\ast\sigma)+\mu`

Substitute:

• -1.2 for z

,

• 3 for σ

,

• 67.9 for μ.

Hence, we have:

`x=(-1.2\ast3)+67.9`

Solving further:

`\begin{gathered} x=-3.6+67.9 \\ x=64.3 \end{gathered}`

Therefore, the HDL level that corresponds to a z-score of -1.2 is 64.3

(b) z = 1.36

We have:

`\begin{gathered} x=(z\ast\sigma)+\mu \\ \\ x=(1.36\cdot3)+67.9 \\ \\ x=71.98\approx72.0 \end{gathered}`

Therefore, the HDL level that corresponds to a z-score of 1.36 is 71.98

ANSWER:

(a) 64.3

(b) 72.0