Normal Distribution pRactice

Between what two standard deviations of a normal distribution contain 68% 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

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%

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434 Company pack 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 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

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? in percentage...

• 5

• 16

• 24

• 32

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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. What is the z-score for 1200 pounds? What percentile is this?

• z=2.27, 99th percentile

• z-=2.27, 1st percentile

• z=-2.27, 1st percentile

• z=-2.27, 99th percentile

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CCSS.HSS.ID.A.4

Scored on a certain standardized test have a mean of 500, and a standard deviation of 100. What is the z-score for a value of 410? What is the percentile?

• z= 0.9, 82nd percentile

• z= -0.9, 82nd percentile

• z= -0.9, 18th percentile

• z= 0.9, 18th percentile

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A 12 oz. can of soda has a mean volume of 12 oz, with a standard deviation of 0.25 oz. Find the z-score for the 90th percentile. How many ounces would the can have to fall at the 90th percentile?

• z= 1.28, 13 ounces and above

• z= 1.28, 12.32 ounces and above

• z= 1.28. 0.9 ounces and above

• z= -1/28, 12.32 ounces

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At a local high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the z-score for the 80th percentile? What GPA falls at the 80th percentile?

• z= -0.84, A GPA of 3.40

• z= -0,84, A GPA of 0.8

• z= 0.84, A GPA of 3.80

• z= 0.84, A GPA of 3.40

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At a high school, GPAs are normally distributed with a mean of 2.9 and standard deviation of 0.6. What GPA do you need to fall in the top 20%? The top 10%?

• 3.40 and 3.67

• 3.67 and 3.40

• 3.80 and 3.90

• 3.20 and 3.10

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CCSS.HSS.ID.A.4