Normal Distribution and Empirical Rule

What shape is a normal distribution curve?

• Half curve
• Round curve
• Bell curve
• Square curve

According to the empirical rule, what percentage of data falls within 1 standard deviation? 

• 25%
• 68%
• 95%
• 99.7%

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CCSS.HSS.ID.A.4

Which of the following is a disadvantage of the Empirical Rule?

• There is no result for 3 standard deviations.

• It is very conservative.

• There is no result for 1 standard deviation.

• The data has to be approximately normal.

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CCSS.HSS.ID.A.4

In a survey of men in the United States (ages 20-29), the mean height was 69.6 inches with a standard deviation of 3.0 inches. Find the minimum height in the top 22%.

• 69.37 in 
• 67.58 in 
• 73.12 in 

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CCSS.HSS.ID.A.4

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 

• 81.5%
• 47.5%
• 68%
• 95%

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CCSS.HSS.ID.A.4

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

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%

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CCSS.HSS.ID.A.4

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.

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CCSS.HSS.ID.A.4

The hourly pay for registered nurses is normally distributed. The average hourly wage for registered nurses is $32.75 with a standard deviation of $4.25.

What percent of registered nurses make between $28.50 and $37 an hour?

• 95%

• 84%

• 99.7%

• 68%

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CCSS.HSS.ID.A.4

ACT Scores are normally distributed. The average score last year was 20.8 with a standard deviation of 3.9.

What percent of students scored above 20.8?

• 34%

• 50%

• 68%

• 47%

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CCSS.HSS.ID.A.4