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:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Here, we are to solve for x.
Rewrite the formula for x.
[tex]x=(z\ast\sigma)+\mu[/tex]
Substitute:
• -1.2 for z
,
• 3 for σ
,
• 67.9 for μ.
Hence, we have:
[tex]x=(-1.2\ast3)+67.9[/tex]
Solving further:
[tex]\begin{gathered} x=-3.6+67.9 \\ x=64.3 \end{gathered}[/tex]
Therefore, the HDL level that corresponds to a z-score of -1.2 is 64.3
(b) z = 1.36
We have:
[tex]\begin{gathered} x=(z\ast\sigma)+\mu \\ \\ x=(1.36\cdot3)+67.9 \\ \\ x=71.98\approx72.0 \end{gathered}[/tex]
Therefore, the HDL level that corresponds to a z-score of 1.36 is 71.98
ANSWER:
(a) 64.3
(b) 72.0
