13.2 Relative Standing (z-scores and percentiles)

What is the formula to find the z-score for population?

• $z=x-\mu$

• $z=\frac{\sigma-\mu}{x}$

• $z=\frac{\sigma}{\sqrt{n}}$

• $z=\frac{x-\mu}{\sigma}$

Tags

CCSS.HSS.ID.A.4

Which of the following is a formula that describes calculating a z-score?

• Z = (score - mean) / stand. devation

• Z = (mean - score) / stand. dev.

• Z = score/stand. dev/ mean

• Z = dragonball

Tags

CCSS.HSS.ID.A.4

What is the purpose of z-scores?

• to describe the exact location of a score within a distribution

• to find the mean of the distribution

• to describe the shape of the distribution

• to find the standard deviation of the distribution

Tags

CCSS.HSS.ID.A.4

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

• True

• False

Tags

CCSS.HSS.ID.A.4

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Tags

CCSS.HSS.ID.A.4

If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what is the z score of a 3rd grader who is 47 inches tall? 

• -5
• -2
• 2
• 5

Tags

CCSS.HSS.ID.A.4

Adam's Z-score on a test is +2.50. What does this mean?

• Adam's score has a 2.5% chance of being better than any other randomly selected score.

• Adam's test score was better than 25% of his peers.

• He scored 2.5 standard deviations above the average.

• He did terrible.

Tags

CCSS.HSS.ID.A.4

What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the standard deviation was 275?

• -1.90

• -1.09

• +1.09

• +1.90

Tags

CCSS.HSS.ID.A.4

Find the mean.

Z-score = -1.4

Standard Deviation: 7

x = 20

• 29.8

• 10.2

• -21

• 35

Tags

CCSS.HSS.ID.A.4

If I tell you that you scored at the 55th percentile on your final exam, you would know:

• 55% of the class scored the same or worse than you did

• You earned a 55% on the exam

• You failed the exam

• 45% of the class scored worse than you did

Tags

CCSS.7.EE.B.3