Normal Distribution and Z-Scores

Find the z-score for 75 given a mean of 60 and a standard deviation of 6.

• -2.5

• 2.5

• -1.15

• 1.15

Find the z-score for 48 given a mean of 50 and a standard deviation of 5.

• 2.5

• -2.5

• -0.4

• 0.4

Find the z-score for 258 given a mean of 273 and a standard deviation of 5.

• 3

• -2

• 2

• -3

Find the z-score for 62 given a mean of 30 and a standard deviation of 20.

• 1.6

• -1.6

• 11.6

• -11.6

What percentage of scores falls within 3 standard deviations of the mean?

• 68%

• 34%

• 99.7%

• 95%

IQ tests have a mean of 100 and SD of 16. Einstein's IQ was 160. What is the z-score of his IQ?

• 1.75

• 3.75

• 0.75

• 2.75

Z-score of 2.5 on an IQ test is considered a genius (mean=100, SD=16). What score makes someone a genius? Hint: SOLVE for X

• 89.2

• 130

• 99.38

• 140

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores?

• Jack’s z = 1.07; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 1.07; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.94; Jill’s z = 1.11; Jill wins the contest

• Jack’s z = 0.94; Jill’s z = 0.90; Jack wins the contest

• Jack’s z = 0.81; Jill’s z = 0.99; Jill wins the contest

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

• True

• False

Find the Z-score.

Mean = 21

Standard Deviation: 1.3

x = 22

• 0.77

• 5.33

• 1.07

• 1.26