Empirical Rule and Chebyshev's Theorem

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. Approximately 95% of molds filled by this machine will hold weights in what interval? 

• 1084 to 1216 pounds 
• 1106 to 1150 pounds 
• 1106 to 1194 pounds 
• 1128 to 1172 pounds

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CCSS.HSS.ID.A.4

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 std dev. 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 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

Which interval shows 68% of the data given a mean of 19 and a standard deviation of 2.5? (empirical)

• 14 to 24
• 11.5 to 26.5 
• 16.5 to 21.5 
• 17 to 21

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CCSS.HSS.ID.A.4

True or false: A normal curve is symmetric

• True
• False

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3? (empirical)

• 9 to 21
• 12 to 18
• 6 to 24
• 13 to 16

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CCSS.HSS.ID.A.4

What does the "k" in Chebyshev's Theorem represent?

• Standard deviation
• The number of standard deviations from the mean
• Variance
• The number of standard deviations from the median

400 books were selected at random from a library. If the mean length of books in this sample was 300 pages with σ=20, what is the minimum number of books that must be between 200 and 400 pages?
(CHEBYSHEV's)

• 384
• 396
• 75%
• 84%

800 basketball players were selected at random. If their mean height was 78 in. with s=5, at least 650 of these players must have been between...

(Chevy)

• 66.45 and 89.55 in. tall.

• 70.05 and 85.95 in. tall.

• 51.35 and 104.65 in. tall.

• 72.25 and 83.75 in. tall