Question

Sat scores are normally distributed and have a mean of 1000 and a standard deviation of 200

A) find the minimum score you would need to be in the top 15% of all test taker

B) what sat score correspondonds to the 3er quartile

Please help me this is my statistics class finding normal distribución

Answer 1

(A) Z=(X-m)/s where m is the mean=1000 and s the SD=200. X is the score.

The top 15% is the p value when p=1-0.15=0.85 corresponding to Z=1.03643.

So X=1.03643*200+1000=1207.286, or about 1207. This is the minimum SAT score for top 15%.

(B) The quartiles are at 0-25%, 25%-50%, 50%-75%, 75%-100%.

The third quartile is 50%-75%. We need two values of Z to determine the SAT score range: Z=0 for 50%, and Z=0.6745 for 75%.

X=1000 when Z=50%; X=0.6744*200+1000=1134.88 or about 1135 when Z=75%. So the 3rd quartile SAT scores are 1000-1135 approx.