The sample mean for a recent introductory psychology test was 78,and the sample variance was 9.If a student received a score of 82,what was this student's z-score?
A)0.44
B)1.33
C)-1.33
D)-0.44

Question

Quizplus · Accepted Answer

The formula for calculating z-score is:
z = (x - μ) / σ
where x is the individual score, μ is the population mean, and σ is the population standard deviation (in this case, we use the sample standard deviation as an estimate of the population standard deviation).

We are given:

Sample mean (μ) = 78
Sample variance (σ^2) = 9
Score of the student (x) = 82

First we need to calculate the sample standard deviation:
σ = √σ^2 = √9 = 3

Now we can calculate the z-score:
z = (x - μ) / σ
z = (82 - 78) / 3
z = 4 / 3
z = 1.33 (rounded to two decimal places)

Therefore, the z-score for a student who received a score of 82 is 1.33. Answer B is the correct choice.

The Sample Mean for a Recent Introductory Psychology Test Was