NEED HELP please!!!!!

Question

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1086 and a standard deviation of 197. Scores on the ACT test are normally distributed with a mean of 20.3 and a standard deviation of 4.9. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 24-percentile, find the actual SAT score.

SAT score = 

Round answer to a whole number.

What would be the equivalent ACT score for this student?

ACT score = 

Round answer to 1 decimal place.

If a student gets an SAT score of 1283, find the equivalent ACT score.

ACT score = 

Round answer to 1 decimal place

Answer 1

1086 = mean

187 is the standard deviation

1086 + 187 has a z score = 1

1086 - 187 = 899 has a z score =-1 with probability of less than 999 = 16%

899 is the 16th percentile

the 24th percentile is a little larger = 953.4

24th percentile has a z score = .709

.709 times 187 = 132.6

1086-132.6 = 953 = the SAT score that's a 24th percentile

ACT has mean = 20.3, standard deviation 4.9

20.3 -4.9 = 15.4 has z score = -1

24th percentile has z score = -.709

.709 x 4.9 = 3.47.

20.3 -3.47 = 16.83 = ACT score for 24th percentile

1283-1086= 197

197/187 = 1.053 = z score for 1283 score

use a z score calculator or z tables

= about 85th percentile

or use the empirical rule as z is close to 1

68% lie within 1 standard deviation from the mean

50+68/2 = 50+34 = 84th percentile. 1.053 is slightly > 1, and 85 is slightly greater than 84.