Chapter 2 - Normal Distribution

Which correctly describes the density curve shown

• The density curve is symmetric

• The density curve is skewed right

• The density curve is skewed left

• The density curve is Normal

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CCSS.HSS.ID.A.3

The area under normal curve is always 1, regardless of the mean and standard.

• True

• False

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CCSS.HSS.ID.A.4

Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete receives his score report: he got a 63, which placed him at the 73rd percen- tile. This means that

• Pete’s score was below the median.

• Pete did worse than about 63% of the test takers.

• Pete did worse than about 73% of the test takers.

• Pete did better than about 63% of the test takers.

• Pete did better than about 73% of the test takers.

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CCSS.HSS.ID.A.3

CCSS.HSS.ID.B.5

For the Normal distribution shown, the standard deviation is closest to

• 0

• 1

• 2

• 4

• 5

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CCSS.HSS.ID.A.4

Rainwater was collected in water collectors at 30 different sites near an industrial complex, and the amount of acidity (pH level) was measured. The mean and stan- dard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the labora- tory, it was found to be in error. The error can be correctedby adding 0.1 pH units to all of the values and then multi- plying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

• 5.64, 1.44

• 5.64, 1.32

• 5.40, 1.44

• 5.40, 1.32

• 5.64, 1.20

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CCSS.HSS.ID.A.2

The figure shown is the density curve of a distribu- tion. Five of the seven points marked on the density curve make up the five-number summary for this distribution. Which two points are not part of the five-number summary?

• B and E

• C and F

• C and E

• B and F

• A and G

If the heights of American men follow a Normal dis- tribution, and 99.7% have heights between 5′0′′ and 7′0′′, what is your estimate of the standard deviation of the height of American men?

• 1′′

• 3′′

• 4′′

• 6′′

• 12′′

Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard devia- tion was 110. In 2009, the mean was 515 and the standard deviation was 116.

What is the standardized score (z-score) for a student who scored 500 on the old SAT scale?

• −30

• −0.27

• −0.13

• 0.13

• 0.27

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CCSS.HSS.ID.A.4

Jorge’s score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score fall

• between the minimum and the first quartile.

• between the first quartile and the median.

• between the median and the third quartile.

• between the third quartile and the maximum.

• at the mean score for all students.

Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne’s standardized score on the ACT was −0.7. What was Wayne’s actual ACT score?

• 4.2

• −4.2

• 13.8

• 17.3

• 22.2

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CCSS.HSS.ID.A.4

CCSS.HSS.MD.A.2