Normal Distribution

A coffee company packs their coffee in bags marked as 250 g. A large number of packs of coffee were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.

Assuming this data is normally distributed, what percentage of packs are underweight?

• 2.5%

• 3.5%

• 4%

• 5%

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CCSS.HSS.ID.A.4

The ages of the population of people living in the Atlanta area are normally distributed with a mean of 43 and a standard deviation of 14.

The town has a population of 5,000. How many would you expect to be aged between 29 and 57?

This Standard Normal Distribution curve may help you solve this problem.

• 1750

• 3860

• 3400

• 4330

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CCSS.HSS.ID.A.4

68% of the marks in a test are between 51 and 64. Assuming this data is normally distributed, what is the mean and standard deviation?

• Mean: 57

  Standard Deviation: 6.5

• Mean: 57

  Standard Deviation: 7

• Mean: 57.5

  Standard Deviation: 6.5

• Mean: 57.5

  Standard Deviation: 13

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CCSS.HSS.ID.A.4

The heights of male students are Normally distributed with mean 1.7 m and standard deviation 0.2 m

In a population of 400 male students, how many would you expect to have a height between 1.4 m and 1.6 m?

• 24

• 54

• 97

• 100

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CCSS.HSS.ID.A.4

In a survey of men that 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 16.15%.

• 69.37 in

• 67.58 in

• 72.6 in

• 75.6

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CCSS.HSS.ID.A.4

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

According to the empirical rule, how much of the data falls within 3 standard deviations? 

• 25%
• 68%
• 95%
• 99.7%

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CCSS.HSS.ID.A.4

The mean GPA of students in a course at UGA 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

What shape is a normal distribution curve?

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

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CCSS.HSS.ID.A.3

Between what two standard deviations of a normal distribution contain 95% of the data?

• one below and one above

• two below and two above

• two below and zero

• zero and two above

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CCSS.HSS.ID.A.4