Empirical Rule

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

A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.

• 2.5%
• .15%
• 2.35%
• 2.25%

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%

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 2.5% of the students?

• 3.5 or higher

• 4.1 or higher
• 4.5 or higher

• 4.7 or higher

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%

In a population, if the mean is 125 and the standard deviation is 25, how common are values in the 100 – 175 range?

• 68%

• 84%

• 81.5%

• 95%

1.  Which best describes the shaded part of this normal distribution graph?  

• All data that is one or higher.
• All data that is one or more standard deviations above the mean.
• All data that is between 1 and 3.
• All data that is above the mean.

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700?

• 2.5%
• 2.35%
• 16%
• 13.5%

The weights of miniature horses are roughly normally distributed with a mean of 230 pounds and standard deviation of 45 pounds.
What proportion of miniature horses weigh between 95 and 365 pounds? 

• 50%
• 68%
• 95%
• 99.7%