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Leona [35]
3 years ago
13

Sagan scored 1200 on the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 980 and

standard deviation 100. Andrea scored 27 on the ACT. The distribution of ACT scores in a reference population is normally distributed with mean 20 and standard deviation 5. Who performed better on the standardized exams and why?
Advanced Placement (AP)
2 answers:
4vir4ik [10]3 years ago
7 0

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

----------------------------------------------------------------------------------------

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

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.

pav-90 [236]3 years ago
5 0
If Sagan scored 1200 divide 980 divide by 100 =3 Andrea =27 so I think that Andrea has the most then sagan 3×9=27
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