Final answer:
Roberto's z-score is approximately 0.43, which indicates that he scored 0.43 standard deviations above the mean on the nationwide math test.
Step-by-step explanation:
To calculate Roberto's z-score on the nationwide math test, we use the formula for z-score:
z = (X - μ) / σ
Where:
- X is Roberto's score
- μ (mu) is the mean of the test scores
- σ (sigma) is the standard deviation of the test scores
Given:
- X = 75 (Roberto's score)
- μ = 72 (mean score)
- σ = 7 (standard deviation)
Plugging in these values into the formula, we get:
z = (75 - 72) / 7
z = 3 / 7
z ≈ 0.43
Roberto's z-score is approximately 0.43, meaning he scored 0.43 standard deviations above the mean.