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

Tags

CCSS.HSS.ID.A.4

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

Tags

CCSS.HSS.ID.A.4

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%

Tags

CCSS.HSF-LE.A.1B

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%

Tags

CCSS.HSF-LE.A.1B

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?

• 4.1 
• 4.1 or higher
• 4.7
• 4.5 or higher

Tags

CCSS.HSF-LE.A.1B

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.

Tags

CCSS.HSS.ID.A.4

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%

Tags

CCSS.HSF-LE.A.1B

Students pass a test if they score 50% or more.

The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.

Assuming this data is normally distributed, what percentage of students pass the test?

• 5%

• 16%

• 24%

• 32%

Tags

CCSS.HSS.ID.A.4

In a population, if μ=125 (mean) and σ=25 (SD), how common are values in the 100 – 175 range?

• 68%

• 84%

• 81.5%

• 95%

Tags

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.ID.A.4