Mat 143 Statistics Empirical Rule and Z Scores

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 is 3 standard deviations below the mean?

• 12

• 16

• 20

• 21

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

• True

• False

Find the z-scores value corresponding if the location is above the mean by 1/2 standard deviations

• -0.50

• +1.00

• +0.50

• -1.00

If Gonzalo's score is 87, the class average is 82, and the SD is 4, what is Gonzalo's Z-score?

• -1.25

• +1.25

• +1.20

• +1.02

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 = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

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

• -1.25

• +1.25

• 16

• 21

Find the z-score.

Mean: 29.8

Standard Deviation: 7

x = 20

• -1.4

• 10.2

• -21

• 35

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