Math Help Stats, NEED TODAY PLEASE 5.6 !! Question 12

Question

The placement test for a college has scores that are normally distributed with a mean of 450 and a standard deviation of 100. If the college accepts only the top 7% of​ examinees, what is the cutoff score on the test for​ admission?

​z-score	1.0	1.1	1.2	1.3	1.4	1.5	1.6	1.7	1.8	1.9	2.0
Percentile	84.13	86.43	88.49	90.32	91.92	93.32	94.52	95.54	96.41	97.13	97.72
​z-score	2.1	2.2	2.3	2.4	2.5	2.6	2.7	2.8	2.9	3.0	3.5
Percentile	98.21	98.61	98.93	99.18	99.38	99.53	99.65	99.74	99.81	99.87	99.98

Answer 1

Top 7% means 93% of the students are not going to be admitted right? so what is the Z score for 93%? looking at the table you see it is about 1.5. Using this Z value (following equation Z = (x - mu)/sigma - look here: https://www.thoughtco.com/z-score-formula-3126281) you can find the cut-off score which will be 100 x 1.5 +450 = 600

Answer 2

use the Z-score formula: Z = (X -mean)/SD.

In the given table, the z-score corresponding to the top 7% is the 93rd percentile --- closest value is Z=1.5

1.5 = (X - 450)/100, where X= cutoff score = 93rd percentile

Solve for X and you should get 600.(Exact value ~ 597.58)