Suppose scores on the mathematics section of the SAT follow a normal distribution with mean 540 and standard deviation 120. ACT math scores are normally distributed with a mean of 18 and a standard deviation of 8. What score on the ACT is equivalent to a score of 750 on the SAT? Give your answer as a whole number, e.g., 13
32
Z = (score-mean)/SD
Find the Z score for 750 on SAT.
Insert that Z score with the data for the ACT to find the equivalent score.
To find the equivalent score on the ACT, we need to use the concept of z-scores. A z-score represents the number of standard deviations a data point is away from the mean.
First, we need to convert the SAT score of 750 into a z-score using the formula:
z = (X - μ) / σ
where X is the SAT score, μ is the mean, and σ is the standard deviation.
For the SAT score of 750:
z_SAT = (750 - 540) / 120
z_SAT = 210 / 120
z_SAT = 1.75
Now, we can use the z-score from the SAT to find the equivalent ACT score. The formula to convert z-scores to an actual data point is:
X = z * σ + μ
where X is the data point, z is the z-score, σ is the standard deviation, and μ is the mean.
For the ACT score:
X_ACT = 1.75 * 8 + 18
X_ACT = 14 + 18
X_ACT = 32
Therefore, the equivalent ACT score to a SAT score of 750 is 32.