Question

Standard IQ scores have a mean of 100 and a standard deviation of 15. When Gabby was in 10th grade, Her IQ was measured to be 60. When she was in 11th grade, it was

measured to be 80. Her psychologist wants to express Gabby's IQ in terms of a z-score. To do so, the psychologist takes the average of the two scores (the one from 10th
grade and the one from 11th grade) and then computes the z-score. What will the z-score of Gabby IQ be?

Answer 1

Step-by-step explanation:

To calculate the z-score of Gabby's IQ, we need to determine the average of her IQ scores and then use the formula for calculating the z-score.

Average of Gabby's IQ scores:

(60 + 80) / 2 = 140 / 2 = 70

Now we can calculate the z-score using the formula:

z = (x - μ) / σ

where:

x = Gabby's IQ score (70 in this case)

μ = Mean IQ score (100)

σ = Standard deviation (15)

Substituting the values into the formula:

z = (70 - 100) / 15

z = -30 / 15

z = -2

Therefore, the z-score of Gabby's IQ will be -2.