Question

38. A doctor measured serum HDL levels in her patients, and found that they were normally distributed with a mean of 69.9 and a standard deviation of 3.6. Find the serum HDL levels that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.(a) z = -1.15(b) z = 2.95

Answer 1

at Z = -1.15, serum HDL levels (x) = 65.76

at Z = 2.95, serum HDL levels (x) = 80.52

STEP BY STEP EXPLANATION

Step 1: at Z = -1.15

`\begin{gathered} z-\text{score = }\frac{data\text{ value - mean}}{s\tan dard\text{ deviation}} \\ -1.15\text{ = }\frac{x\text{ - 69.9}}{3.6} \\ x\text{ - 69.9 = -1.15}\ast3.6 \\ x\text{ = -4.14 + 69.9} \\ x\text{ = 65.76} \end{gathered}`

Step 2: at Z = 2.95

`\begin{gathered} 2.95\text{ = }\frac{x\text{ - 69.9}}{3.6} \\ x\text{ - 69.9 = 2.95}\ast3.6 \\ x\text{ = 10.65 + 69.9} \\ x\text{ = 80.52} \end{gathered}`