MATH 108



MATH 109 Worksheet : Normal Approximation

Part 1 : You have data on the IQ scores of 3rd graders tested nationally. You find that the IQ scores are normally distributed with an average of 100 and a standard deviation of 15.

1. Approximately what percent of IQ scores are between 85 and 115 ?

2. Approximately what percent of IQ scores are greater that 85 ?

3. Approximately what percent of IQ scores are between 79 and 133 ?

4. Approximately what percent of IQ scores are less than 79 ?

5. Approximately what percent of IQ scores are between 115 and 133 ?

6. Approximately what percent of IQ scores are exactly 100 ?

7. Approximately what percent of IQ scores are exactly 79 ?

8. Approximately what is the percentile rank for a raw score of 100 ?

9. Approximately what is the percentile for a raw score of 133

10. Approximately what is the 50%-tile IQ score ?

11. Approximately what is the 90%-tile IQ score ?

12. Approximately what is the 30%-tile IQ score ?

13. Approximately what is the 75%-tile IQ score ?

14. Approximately what is the 25%-tile IQ score ?

15. Approximately what is the Interquartile Range of IQ scores ?

16. Approximately what percent of IQ scores are greater than 150 ?

17. Approximately what percent of IQ scores are greater than 190 ?

Part 2 : The weights of a large population of college males are normally distributed with an average of 173 pounds and a standard deviation of 20 pounds.

1. What percent of college males weigh between 166 lb. and 180 lb. ?

2. What percent of college males weigh more than 180 lb.?

3. What percent of college males weigh between 150 lb. And 180 lb. ?

4. What percent of college males weigh exactly 152 lb.?

5. What percent of college males weigh less than 200 lb.?

6. What is the 30%-tile weight for college males ?

7. Approximate the percentile rank for a college male who weighs 190 lb.

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