Empirical Rule and Z-Score

In a normal distribution, what percent of the values lie within three standard deviations of the mean?

(from z = -3 to z = 3)

• 99.7%

• 81.5%

• 95%

• 68%

In a normal distribution, what percent of the values lie within one standard deviation of the mean?

(from z = -1 to z = 1)

• 13.5%

• 34%

• 95%

• 68%

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score has a z-score of 1?

• 20

• 24

• 25

• 28

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What percent of ACT scores are less than 32?

• 81.5%

• 95%

• 97.5%

• 99.7%

Find the z-score. Mean: 16 Standard Deviation: 4 x = 11

• -1.25

• +1.25

• 16

• 21

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

Find the z-score.

Mean: 29.8

Standard Deviation: 7

x = 20

• -1.4

• 10.2

• -21

• 35

Find the z-score.

Mean = 45

Standard Deviation: 2.1

x = 50

• 2.38

• 3.00

• 3.08

• 2.33

Find the z-score.

Mean: 22.8

Standard Deviation: 7

x = 20

• -0.4

• 17.2

• 22.04

• 32.5

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26