M3R 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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CCSS.HSS.ID.A.4

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

A company makes parts for a machine. The lengths of the parts must be within certain limits or they will be rejected.

A large number of parts were measured and the mean and standard deviation were calculated as 3.1 m and 0.005 m respectively.

Assuming this data is normally distributed and 99.7% of the parts were accepted, what are the limits?

• Between 3.075 m and 3.125 m

• Between 3.080 m and 3.120 m

• Between 3.085 m and 3.115 m

• Between 3.090 m and 3.110 m

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

The ages of the population of people living in Meru area in Ipoh are Normally distributed with mean 43 and standard deviation 14

The town has a population of 5,000.

How many would you expect to be aged between 22 and 57?

You can use this Standard Normal Distribution curve:

• 1750

• 3860

• 3870

• 4330

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

The mean July daily rainfall in Hulu Kinta is 10 mm and the standard deviation is 1.5 mm

Assume that this data is normally distributed.

How many days in July would you expect the daily rainfall to be less than 8.5 mm?

• 5

• 6

• 7

• 10

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

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 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?

• -1.33
• 1.33
• 0.88
• 1.02

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CCSS.HSS.ID.A.4