The Empirical Rule (68-95-99.7 Rule) for Normal Distributions

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

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.
• 24,000 km and 34,000 km.
• 26,000 km and 34,000 km.
• 27,000 km and 31,000 km.

Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21
• 12 to 18
• 6 to 24
• 13 to 16

Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21
• 12 to 18
• 6 to 24
• 13 to 16

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3?

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

What percent of the data falls within 3 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

What percent of the data falls within 2 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

What percent of the data falls within 1 standard deviation of the mean?

• 99.7

• 34

• 68

• 95

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%
• 34%
• 16%
• 2.5%

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%