Z-score and Data Type

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

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

A data set has a mean of 20 and a standard deviation of 3. Calculate the z-score for 23.

Tags

CCSS.HSS.ID.A.4

Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches.  The z score corresponding to a woman with a height is 2.56. How tall is the woman?

• 24.42 in
• 70 in
• 28in
• 68.6in

Tags

CCSS.HSS.ID.A.4

Find the z-score.

Mean = 25

Standard Deviation: 7

x = 9.6

• –2.2

• –36

• 5.2

• 23.46

Tags

CCSS.HSS.ID.A.4

Use the image of the normal graph provided. What is the value of the standard deviation?

• 6

• 12

• 36

• 18

Tags

CCSS.HSS.ID.A.4

CCSS.HSS.ID.A.2

What is the correct formula to find the z-score?

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score is 3 standard deviations below the mean?

• 12

• 16

• 20

• 21

Tags

CCSS.HSS.ID.A.4

In a normal distribution, what percent of the values lie above the mean?

• 13.5%

• 34%

• 50%

• 68%

Tags

CCSS.6.SP.A.2

Ashley want to classify the following from the data set, 322

30, 171, 184, 201, 212, 250, 265, 270, 272, 289, 305, 306, 322, 322, 336, 346, 351, 370, 390, 404, 409, 411, 436, 437, 439, 441, 444, 448, 451, 453, 470, 480, 482, 487, 494, 495, 499, 503, 514, 521, 522, 527, 548, 550, 559, 560, 570, 572, 574, 578, 585, 592, 592, 607, 616, 618, 621, 629, 637, 638, 640, 656, 668, 707, 709, 719, 737, 739, 752, 758, 766, 792, 792, 794, 802, 818, 830, 832, 843, 858, 860, 869, 918, 925, 953, 991, 1000, 1005, 1068, 1441

She found that the mean was 576.1 and the standard deviation is 236.3

• Normal Data

• Unusual Data

• Outlier

Answer explanation

use the mean to find the standard devotion away. Then look at where it falls:

Normal ( between mean and 2σ) ,

Unusual ( between 2σ and 3σ) and

Outlier (passed 3σ)