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Math Coach Amy
Amy Ferguson Moncure

H Algebra 2/Trig ยท Unit 8

Inverse Normal

Given a percent, find the cutoff score. Use RIGHT when the percent is a top percent.

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Key Ideas Easy Medium Hard

invNorm(area, mean, standard deviation) reads from the left.

A top percent uses RIGHT.

Round the score to the nearest tenth.

What to Remember

Area on the left

invNorm(area, mean, standard deviation) returns the score that has that area below it.

A top percent

For the top 15%, the area on the right is 0.15.

Use invNorm(0.15, mean, standard deviation, RIGHT).

Level 1

Easy

A percent below the score

Example
Scores are normally distributed with mean 78 and standard deviation 5. What score has 20% of the scores below it? Round to the nearest tenth.

The percent below a score is the area on the left.

invNorm(0.2, 78, 5)

The calculator value to three decimal places is 73.792.

Round to the nearest tenth.

73.8

Answer: 73.8

1
Times are normally distributed with mean 90 seconds and standard deviation 8 seconds. What time has 25% of the times below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.25, 90, 8)

The calculator value to three decimal places is 84.604.

Round to the nearest tenth.

84.6

Answer: 84.6

2
Weights are normally distributed with mean 64 ounces and standard deviation 5 ounces. What weight has 10% of the weights below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.1, 64, 5)

The calculator value to three decimal places is 57.592.

Round to the nearest tenth.

57.6

Answer: 57.6

3
Heights are normally distributed with mean 50 inches and standard deviation 4 inches. What height has 30% of the heights below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.3, 50, 4)

The calculator value to three decimal places is 47.902.

Round to the nearest tenth.

47.9

Answer: 47.9

4
Scores are normally distributed with mean 82 and standard deviation 10. What score has 15% of the scores below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.15, 82, 10)

The calculator value to three decimal places is 71.636.

Round to the nearest tenth.

71.6

Answer: 71.6

5
Pages are normally distributed with mean 36 and standard deviation 7. What length has 40% of the essays below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.4, 36, 7)

The calculator value to three decimal places is 34.227.

Round to the nearest tenth.

34.2

Answer: 34.2

Level 2

Medium

A top percent

Example
Scores are normally distributed with mean 84 and standard deviation 6. What score is the top 10%? Round to the nearest tenth.

A top percent is the area on the right.

invNorm(0.1, 84, 6, RIGHT)

The calculator value to three decimal places is 91.689.

Round to the nearest tenth.

91.7

Answer: 91.7

1
Times are normally distributed with mean 70 minutes and standard deviation 12 minutes. What time is the top 15%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.15, 70, 12, RIGHT)

The calculator value to three decimal places is 82.437.

Round to the nearest tenth.

82.4

Answer: 82.4

2
Weights are normally distributed with mean 56 pounds and standard deviation 5 pounds. What weight is the top 20%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.2, 56, 5, RIGHT)

The calculator value to three decimal places is 60.208.

Round to the nearest tenth.

60.2

Answer: 60.2

3
Points are normally distributed with mean 100 and standard deviation 9. What score is the top 5%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.05, 100, 9, RIGHT)

The calculator value to three decimal places is 114.804.

Round to the nearest tenth.

114.8

Answer: 114.8

4
Lengths are normally distributed with mean 44 cm and standard deviation 8 cm. What length is the top 25%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.25, 44, 8, RIGHT)

The calculator value to three decimal places is 49.396.

Round to the nearest tenth.

49.4

Answer: 49.4

5
Temperatures are normally distributed with mean 86 degrees and standard deviation 5 degrees. What temperature is the top 12%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.12, 86, 5, RIGHT)

The calculator value to three decimal places is 91.875.

Round to the nearest tenth.

91.9

Answer: 91.9

Level 3

Hard

A less familiar percent

Example
Scores are normally distributed with mean 75 and standard deviation 11. What score has 8% of the scores below it? Round to the nearest tenth.

The percent below a score is the area on the left.

invNorm(0.08, 75, 11)

The calculator value to three decimal places is 59.544.

Round to the nearest tenth.

59.5

Answer: 59.5

1
Times are normally distributed with mean 63 minutes and standard deviation 7 minutes. What time is the top 18%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.18, 63, 7, RIGHT)

The calculator value to three decimal places is 69.408.

Round to the nearest tenth.

69.4

Answer: 69.4

2
Weights are normally distributed with mean 48 ounces and standard deviation 9 ounces. What weight has 35% of the weights below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.35, 48, 9)

The calculator value to three decimal places is 44.532.

Round to the nearest tenth.

44.5

Answer: 44.5

3
Distances are normally distributed with mean 110 meters and standard deviation 14 meters. What distance is the top 6%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.06, 110, 14, RIGHT)

The calculator value to three decimal places is 131.767.

Round to the nearest tenth.

131.8

Answer: 131.8

4
Pages are normally distributed with mean 54 and standard deviation 5. What length has 22% of the reports below it? Round to the nearest tenth.
Show Answer

The percent below a score is the area on the left.

invNorm(0.22, 54, 5)

The calculator value to three decimal places is 50.139.

Round to the nearest tenth.

50.1

Answer: 50.1

5
Scores are normally distributed with mean 88 and standard deviation 13. What score is the top 16%? Round to the nearest tenth.
Show Answer

A top percent is the area on the right.

invNorm(0.16, 88, 13, RIGHT)

The calculator value to three decimal places is 100.928.

Round to the nearest tenth.

100.9

Answer: 100.9

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