Question

each year thousands of high - school students take either the sat or the act, standardized tests used in the college admissions process. combined sat math and verbal scores go as high as 1600, while the maximum act composite score is 36. since the two exams use very different scales, comparisons of performance are difficult. a convenient rule of thumb is sat = 40×act + 150, that is, multiply an act score by 40 and add 150 points to estimate the equivalent sat score. an admissions officer reported the following statistics about the act scores of 2328 students who applied to her college one year. find the summaries of equivalent sat scores.
lowest score = 17 mean = 28 standard deviation = 2
q3 = 31 median = 29 iqr = 4
lowest score for the sat = 830
mean for the sat =

Explanation:

Step1: Recall the conversion formula

The formula to convert ACT score to SAT score is $SAT = 40\times ACT+150$.

Step2: Calculate the mean of SAT scores

We know the mean of ACT scores is $\bar{x}_{ACT}=28$. Substitute it into the formula:
$SAT = 40\times28 + 150$.
First, calculate $40\times28=1120$. Then, $1120 + 150=1270$.

Answer:

1270