Finding Z-Scores, Standard Deviation, Mean and X

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

Find the z-score value corresponding if the location is below the mean by 2 standard deviations

• +2.00

• -2.00

• +1.25

• -1.00

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

• True

• False

z-scores is the standardized scores for X values

• True

• False

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

• 2.26

• 16.45

• -2.26

• 1.26

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26

Find the z-scores value corresponding if the location is above the mean by 1/2 standard deviations

• -0.50

• +1.00

• +0.50

• -1.00

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

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.

A scientist planted two groups of seedlings. After six months, she found that the heights for both groups were normally distributed with means and standard deviations as follows:

Group A: Mean = 41.7 cm, Standard Deviation = 2.2 cm

Group B: Mean = 38.6 cm, Standard Deviation = 3.4 cm

For which group does a z-score of 1.5 give a taller plant?

• Group A - 45 cm

• Group A - 43.2 cm

• Group B - 43.7 cm

• Group B - 42 cm