Question

A test involving 310 men ages 20 to 24 found that their blood cholesterol levels had a mean of 183 mg/dl and a standard deviation of 44.8 mg/dl. A. determine the z-score, to the nearest hundredth, for one of the men who had a blood cholesterol level of 219 mg/dl. B. the z-score for one man was -1.51. What was his blood cholesterol level? Round to the nearest hundredth.

Answer 1

Answer:

A) z-score = 0.80

B) The man's blood cholesterol level = 115.35 mg/dl

Explanations:
`\text{The mean, }\bar{x}\text{ = 183}`

For the man who has a cholesterol level of 219 mg/dl, x = 219 mg/dl

Standard deviation, σ = 44.8 mg/dl

The z-score is given by the formula:

`\begin{gathered} z-score\text{ = }\frac{x-\bar{x}}{\sigma} \\ z-\text{score = }(219-183)/(44.8) \\ z-\text{score = }0.80 \end{gathered}`

B) z-score = -1.51

The man's blood cholesterol level, x = ?

`\begin{gathered} z-\text{score = }\frac{x-\bar{x}}{\sigma} \\ -1.51\text{ = }(x-183)/(44.8) \\ -1.51(44.8)\text{ = x - 183} \\ -67.648\text{ = }x\text{ - 183} \\ x\text{ = -67.648+183} \\ \text{x = }115.35 \end{gathered}`