Question

Serum cholesterol levels were taken from a population of male college students. The results were normally distributed with a mean of 200 and a standard deviation of 10.15. Convert the following into z-scores: a) x = 172 b) x = 192 c) x = 184 d) x = 212

Answer 1

Solution

z = (x - ) /

(a)

x = 172

z = (172 - 200) / 10.15 = -2.76

(b)

x = 192

z = (192 - 200) / 10.15 = -0.79

(c)

x = 184

z = (184 - 200) / 10.15 = -1.58

(d)

x = 212

z = (212 - 200) / 10.15 = 1.18

Answer 2

To convert the given values into z-scores, we can use the formula:

z = (x - μ) / σ

Where:

• z is the z-score

• x is the given value

• μ is the mean of the distribution

• σ is the standard deviation of the distribution

Given: Mean (μ) = 200 Standard deviation (σ) = 10.15

Let's calculate the z-scores for each value:

a) x = 172 z = (172 - 200) / 10.15 z = -2.753

b) x = 192 z = (192 - 200) / 10.15 z = -0.788

c) x = 184 z = (184 - 200) / 10.15 z = -1.574

d) x = 212 z = (212 - 200) / 10.15 z = 1.180

So the z-scores for the given values are: a) z = -2.753 b) z = -0.788 c) z = -1.574 d) z = 1.180