Answer: A.
Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.
SAT Score Distribution
the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 980
standard deviation ( sd )= 100
we knows that Sagan scored 1200 on the SAT
P(X = 1200) = (1200-980)/100
= 220/100= 2.2
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ACT Score Distribution
mean ( u ) = 20
standard deviation ( sd )= 5
Andrea scored 27 on the ACT
P(X = 27) = (27-20)/5
= 7/5= 1.4
Step-by-step explanation:
a. Sagan scored higher than Andrea. Sagan's standardized score was 2.2, which is 2.2 standard deviations above the mean and Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean.
b. Sagan scored higher than Andrea. Sagan's score was a 1200, which is greater than Andrea's score of 27.
c. Andrea scored higher than Sagan. Andrea's standardized score was 1.4, which is 1.4 standard deviations above the mean but closer to the mean than Sagan's standardized score of 2.2 standard deviations above the mean.
d. Sagan scored higher than Andrea. Sagan's score was 220 points above the mean of 980 and Andrea's was 7 points above the mean of 20.
e. Andrea scored higher than Sagan. Andrea is only 9 points from the top score of 36 on the ACT and Sagan is 400 points from the top score of 1600 on the SAT.