Normal Distributions

What shape is a normal distribution curve?

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

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CCSS.HSS.ID.A.3

This data is normally distributed.  What percent of the data is in the shaded region?

• 5%
• 95%
• 2.5%
• 50%

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.1

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

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

Given: Mean = 10, standard deviation = 2.
What is the probability that the data will be between 8 and 12? 

• 99.7%
• 68%
• 67%
• 95%

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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

The average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  

• 2
• 1
• -2
• -1

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CCSS.HSS.ID.A.4

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees.  What is the z-score for a temperature of 17 degrees?  

• 1 
• 1.43
• -1.43
• 11.5

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CCSS.HSS.ID.A.4

Pat and Chris both took a spatial abilities test (mean = 80, std. dev. = 8).  Pat scores a 76 and Chris scored a 94.  What percent of individuals would score between Pat and Chris? 

• 26.8%
• 96%
• 65.1%
• 4%

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.1

The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and 𝞂 = 15.

Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?

• 115
• 130.75
• 145
• 120

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CCSS.HSS.ID.A.4