Question

Composite score on the ACT and the SAT are normally distributed. Mary scored 26 on the ACT and 1200 on the SAT. Numerical summaries are shown in the table below. Interpret the probabilities and determine on which test Jane performed better.

test/summary	Mean	Standard deviation	Probabilities
ACT	21.1	5.1	P( X greater than or equal to 26)= 0.1685
SAT	1026	210	P (X greater than or equal to 1200) =0.2033

Answer 1

score on the ACT and the SAT are normally distributed.

Here we need to calculate the z score

for ACT Z= 1200-1026/210=0.83

for SAT Z=26-21.1/5.1=0.96

since the Z score for SAT is high as compared to ACT we can conclude that Jane performed better in SAT