Z-score

z scores act as a ruler by placing scores on a standard scale.

• True

• False

Z-score represents the standard deviation in mean units.

• True

• False

We express our z scores as percentages only when our data are

• Normally distributed

• Highly skewed

• Measured on an ordinal scale

• Standardized

You receive a negative z score on a test. This indicates that:

• Everyone in the sample had a higher score.

• Your professor curved the scores.

• Your score is in the lower half of the distribution.

• You are above the mean on most tests, but not this one.

You receive a z score of 0 on a test. This tells you that:

• There was a floor effect on the exam.

• You had an average score.

• It was a very difficult exam.

• you did very poorly on the test; no answers were correct

The life of a particular cosmetic product is normally distributed with a mean of 12 months and a standard deviation of 3 months. About what percent of the products last between 12 and 15 months?

• 68%

• 34%

• 16%

• 2.5%

Girl’s heights in a class are normally distributed with a mean of 63.6 inches 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

• 28.5 in

• 68.6 in

• 70 in

In a factory, the weight of a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of this machine will hold weights in what interval?

• 1084 to 1216 pounds

• 1106 to 1150 pounds

• 1106 to 1194 pounds

• 1128 to 1172 pounds

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

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?

• -1

• 3

• 2

• -2