THe Empirical Rule

AP Stats

Between -1 deviation and the mean

Between -1 deviation and the mean

Where does 34% of the area of this normal curve lie?

Between +1 and +2 deviations

Where Does 13.5% of the area of this normal curve lie?

Between -2 and -3 devations

Where Does 2.35% of the area of this normal curve lie?

Above +3 deviations

Where does 0.15% of the area of this normal curve lie?

Within 1 Standard Deviation of the Mean; The Red Zone

Where can you find 68% of the area of this normal curve?

Within 2 Standard Deviations of the Mean; The Red and Green Zones Combined

Where can you find 95% of the area of this normal curve?

Within 3 Standard Deviations of the Mean; The Red, Green, and Blue Zones Combined

Where Can You Find 99.7% of the area of this normal curve?

34

You are +1 standard deviation away from the mean. This is ___% of the area of the normal curve.

47.5

You are +2 standard deviations away from the mean. This is ___% of the area of the normal curve.

49.85

You are +3 standard deviations away from the mean. This is ___% of the area of the normal curve.

0.15

You are beyond +3 standard deviations away from the mean. This is ___% of the area of the normal curve.

34

You are -1 standard deviation away from the mean. This is ___% of the area of the normal curve.

+2 or -2

You are ___ standard deviation(s) away from the mean. This accounts for 47.5% of the area of a normal curve.

+1 or -1

You are ___ standard deviation(s) away from the mean. This accounts for 34% of the area of a normal curve.

Above +3 or Below -3

You are ___ standard deviations away from the mean. This is 0.15% of the area of the normal curve.

16

You are below -1 deviation. This is ___% of the area of the normal curve.

2.5

You are above +2 standard deviations. This is ___% of the area of the normal curve.

1

68% of the area of a normal curve within ___ standard deviation(s) away from the mean.

2

95% of the area of a normal curve is within ___ standard deviation(s) away from the mean.

95

______% of the area of a normal curve is 2 standard deviations away from the mean.

3

99.7% of the area of a normal curve is ___ standard deviation(s) away from the mean.

68

1 standard deviation of the mean accounts for ___% of the area of a normal curve.

99.7

3 standard deviations of the mean accounts for ___% of the area of a normal curve.

x̄

The mean of a sample

s

The standard deviation of a sample

σ

The standard deviation of a population

μ

The mean of a population

Skewed Distributions

Use the median and IQR for center and spread

Normal Distributions

Use the mean and standard deviation for center and spread.

Mean = 100, S.D. = 10. 68% of the values will be between which two numbers?

90 and 110

Mean = 100 S.D. = 10. 95% of the values will be between which two numbers?

80 and 120

Mean = 100 S.D. = 10. 99.7% of the values will be between which two numbers?

70 and 130

Mean = 100 S. D. = 10. The value 115 is how many deviations from the mean?

+1.5

Mean = 100 S. D. = 10. The value 95 is how many deviations from the mean?

-0.5

Mean = 100 S.D. = 10. 34% of the values will be between which two numbers?

90 and 100

Mean = 100 S. D. = 10. The value 123 is how many deviations from the mean?

+2.3

Mean = 100 S. D. = 10. The value 84 is how many deviations from the mean?

-1.6