Question

A stuby was conducted on students from a particular high schoel over the lant 8 years. The folbwing information was foued regardigg stacdardiced tests used for colloge admiasce Scores on the sar test are normally datributed with a mean of 1085 and a sandard devation or 203 . Scores on the ACT test are nermaly datributed with a mean of 20 and a standard deviation ef 49 it is assumed that the The tests measure the same apthode, but use different scales.

If a student gets an sat score that is the 72 pertentile, find the actual sat score. SAT sare
SAT score _______ .

Answer 1

To find the actual SAT score corresponding to the 72nd percentile, we can convert the percentile to a z-score and use that to calculate the SAT score.

Step-by-step explanation:

To find the actual SAT score corresponding to the 72nd percentile, we need to convert the percentile into a z-score and then use that z-score to find the corresponding SAT score. The formula to convert a percentile to a z-score is:

z = (X - mean) / standard deviation

Plugging in the values for the SAT test, the z-score corresponding to the 72nd percentile is approximately 0.655. So we can calculate the actual SAT score as follows:

SAT score = (z * standard deviation) + mean = (0.655 * 203) + 1085 = 1338.765

Therefore, the actual SAT score corresponding to the 72nd percentile is approximately 1339.