Answer :
Answer:
The z-score for a a class with 21 students is -1.33.
Step-by-step explanation:
The z-score of a raw X is computed by subtracting the mean of a distribution from the raw score X and dividing the result by the standard deviation of the distribution.
The z-scores are standardized scores and follow a Standard normal distribution.
Given:
μ = 38.1
σ = 12.9
X = 21
Compute the z-score for the raw score X as follows:
[tex]z=\frac{X-\mu}{\sigma} =\frac{21-38.1}{12.9} =-1.32558\approx-1.33[/tex]
Thus, the z-score for a a class with 21 students is -1.33.
The z-score for a class with 21 students is approximately -1.33.
To find the z-score for a class with 21 students, given the average class size (mean) of 38.1 students and a standard deviation of 12.9 students, we use the formula:
Z = (X - μ) / σ, where:
X is the value for which we are finding the z-score (in this case, 21 students),μ is the mean (38.1 students), andσ is the standard deviation (12.9 students).
Substituting these values into the formula gives:
Z = (21 - 38.1) / 12.9
Z = -17.1 / 12.9
Z ≈ -1.33
Therefore, the z-score for a class with 21 students is approximately -1.33.
