Z-score, percentile, and empirical rules

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

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 = 27

Standard Deviation: 1.4

x = 11

• -11.43

• 7.85

• -2.33

• 4.16

Find the z-score.

Mean: 22.8

Standard Deviation: 7

x = 20

• -0.4

• 17.2

• 22.04

• 32.5

What percentile is it if I got Z-score of -1.08?

What percentile is it if I got Z-score of -0.05?

What's the Z-score if I'm in the 90th percentile?

What's the Z-score if I'm in the 44th percentile?

What's the Z-score if I'm in the 33th percentile?

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 

• 1084 to 1216 pounds 
• 1106 to 1150 pounds 
• 1106 to 1194 pounds 
• 1128 to 1172 pounds