DAP Empirical Rule, Z-Scores, Percentages and Percentiles

Joanne's score on a test gives her a Z-score is -1.50. What does this mean?

• Joanne didn't take the test yet.

• Joanne's test score is 1.50 standard deviations below the average test score.

• Joanne did better than 1.50 times her peers.

• Joanne's test score, on average, was 1.5 points lower than the other test scores.

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What is the Z-score for Tina if she got a 31 on the ACT, the mean was 23 and the SD was 4?

• +0.20

• +2.00

• -2.00

• -0.20

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What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the SD was 275?

• -1.90
• -1.09
• +1.09
• +1.90

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So if Tina's Z-score is +2.00 and Paula's Z-score is +1.9, who performed better compared to the average?

• Tina's performance is farther above the mean so she did better.

• Paula's score is closer to the mean so she did better.

• They both did the same.

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The most recent test you took had an average of 80 with a SD of 8 points.

If you got a 96, what is your Z-score?

• -2.00

• -0.75

• +2.00

• +1.13

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Which number is not a significant value for the Empirical Rule?

• 65%

• 75%

• 95%

• 99.7%

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A machine produces electrical components.
99.7% of the components have lengths between 1.176 cm and 1.224 cm.
Assuming this data is normally distributed, what are the mean and standard deviation?

• Mean = 1.210 cm
  S.D. = 0.008 cm
• Mean = 1.200 cm
  S.D. = 0.004 cm
• Mean = 1.190 cm
  S.D. = 0.008 cm
  
• Mean = 1.200 cm
  S.D. = 0.008 cm

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

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A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. What is the probability a can will be less than 11.8 oz? Round to the nearest thousandth.

• 0.212

• 0.788

• 0.288

• 0.983

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At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the GPA of the highest 5%?

• 3.592 or higher

• 3.887 or higher

• 4.0

• 2.900 or higher

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