Empirical Rule & Z-Score

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

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%
• 99.7%
• 95%
• 84%

What percentage of data is within 3 standard deviations

• 99.5%

• 68%

• 45%

• 99.7%

What percentage of data is within 2 standard deviations

• 68

• 95

• 99.7

• 2.35

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.

Find the proportion of golfers that are between 30 and 46 years old.

• 68%

• 94%

• 95%

• 99.7%

In a normal distribution, what percent of the values lie above the mean?

• 13.5%

• 34%

• 50%

• 68%

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

• True

• False

Find the z-score value corresponding if the location is below the mean by 2 standard deviations

• +2.00

• -2.00

• +1.25

• -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

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

• +0.2
• +2.0
• -2.0
• -0.2