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Algebra 2 Unit 4 Inferences and Conclusions from Data Performance Task 1
Normal Distribution with SAT Scores
Are you beginning to make college plans? Are you academically prepared for college? This task will help you to see if your
peers are on track for the academic rigor that will be required of those who go off to the world of college. To complete this
task you need to perform the following steps:
The data we collected as a class will be sent to a file on your calculator. Please use the
calculator to help you with the following steps. You may need to use additional paper to
show your work.
Step 3
Calculate the MEAN, VARIANCE, and STANDARD DEVIATION for the class data table for MALE MATH SAT SCORES.
Step 4
Sketch the NORMAL DISTRIBUTION CURVE for the data you found in Step 3.
Step 5
Calculate the MEAN, VARIANCE, and STANDARD DEVIATION for the class data table for FEMALE MATH SAT SCORES.
Step 6
Sketch the NORMAL DISTRIBUTION CURVE for the data you found in Step 5.
Step 7
Calculate the MEAN, VARIANCE, and STANDARD DEVIATION for the class data table for ALL MATH SAT SCORES.
Step 8
Sketch the NORMAL DISTRIBUTION CURVE for the data you found in Step 7.
Step 9
Use the 2014 National SAT Data Table to create a NORMAL DISTRIBUTION CURVE for the OVERALL MEAN SCORES in
MATHEMATICS (Table 1).
Algebra 2 Unit 4 Inferences and Conclusions from Data Performance Task 1
Normal Distribution with SAT Scores
Step 10
Use your NORMAL DISTRIBUTION CURVES to answer the following questions:
1.
Did the males or females have a higher mean score for our class data?
2.
Did the males or females have a larger standard deviation for our class data?
3.
According to our male class data, what is the probability that a randomly selected MALE score at our school is greater
than two standard deviations above the mean?
4.
According to our female class data, what is the probability that a randomly selected FEMALE score at our school is less
than one standard deviation below the mean?
5.
According to our male class data, what is the probability that a randomly selected MALE score at our school is between
one standard deviation from the mean?
6.
Between what scores would a FEMALE student at our school have to receive to remain within one standard deviation
from the mean of all FEMALE scores at our school?
7.
What score would a student have to receive to be considered in the top 2.5% of the population at OUR SCHOOL?
8.
What score would a student have received to be considered in the top 2.5% of the population in 2014?
9.
What score would a student have to receive to be considered in the top 50% of the population at OUR SCHOOL?
10. What score would a student have received to be considered in the top 50% of the population in 2014?
ADVANCED
(90-100%)
☐ Normal Distribution Curves are
sketched for the 2014 SAT data
for both MALE and FEMALE
students (in MATH)
☐ Writes a paragraph comparing
and contrasting the male and
female math SAT scores in our
class data to the national data in
2014
PROFICIENT
(80-89%)
☐ Tables are complete (Steps 1,2)
☐ Mean, Variance, and Standard Deviation
Calculations are correct (Steps 3,5,7)
☐ Normal Distribution Curves are correct for class
data (Steps 4,6,8)
☐ Normal Distribution Curve is correct for 2014 data
(Part 9)
☐ The questions are answered using grammatically
correct complete sentences (Part 10)
☐ Work is neat and well organized
BASIC
(70-79%)
☐ Meets 4-5 of
the “Proficient”
requirements
BELOW BASIC
(0-69%)
☐ Meets fewer than
5 of the
“Proficient”
Requirements