Download Learning Goal: Percentiles with the Normal Distribution Curve

NAME:____________________________________________________
Algebra 2/Trig – Percentiles with the Normal Distribution Curve CLASSWORK
DATE:_________
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DO NOW
1. On a test that has a normal distribution of scores, a score of 57 falls one standard deviation below the mean,
and a score of 81 is two standard deviations above the mean. Determine the mean score of this test.
Learning Goal: Percentiles with the Normal Distribution Curve
The term percentile refers to the percentage of data that lies at or below a certain score.
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For example:
- If you are in the 90th percentile for your height, that means 90% of the sample population had a lower
height than you (i.e. you are taller than 90% of the sample population)
- If you are in the 65th percentile for SAT scores, that means 65% of the sample population had a lower
score than you (i.e. you scored better than 65% of the sample population).
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The mean (at the center peak of the curve) is the 50th percentile.
Adding the given percentages from the chart will let you find certain percentiles along the curve.
REAL-LIFE EXAMPLE WITH PERCENTILES
Two students just received their scores for the SAT exam. Student #1 scored a 1200 and student #2 scored an
1700. The students were told that the mean score was a 1400 and the standard deviation was 200. What are the
percentile ranks for these two students, and what do their percentile ranks mean?
PERCENTILE QUESTIONS
1. On a standardized test, the distribution of scores is normal, the mean of the scores is 75, and the standard
deviation is 5.8. If a student scored 83, the student’s score ranks
(1) below the 75th percentile
(2) between the 75th percentile and the 84th percentile
(3) between the 84th percentile and the 97th percentile
(4) above the 97th percentile
2. On a standardized test, the distribution of scores is normal, the mean of the scores is 505, and the standard
deviation is 90. If a student scored 600, the student’s score ranks
(1) below the 65th percentile
(2) between the 65th percentile and the 80th percentile
(3) between the 80th percentile and the 90th percentile
(4) above the 90th percentile
3. The scores on a 100 point exam are normally distributed with a mean of 80 and a standard deviation of 6. A
student's score places him between the 69th and 70th percentile. Which of the following best represents his
score?
(1) 66
(2) 81
(3) 84
(4) 86
SUMMARY OF NORMAL DISTRIBUTION AND PERCENTILES
Mrs. Ramírez is a real estate broker. Last month, the sale prices of homes in her area approximated a normal
distribution with a mean of $150,000 and a standard deviation of $25,000.
A house had a sale price of $175,000. What is the percentile rank of its sale price, to the nearest whole
number? Explain what that percentile means.
Mrs. Ramírez told a customer that most of the houses sold last month had selling prices between $125,000 and
$175,000. Explain why she is correct.