Normal Distribution and Z Score

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.
Point C on this Normal curve corresponds to

• 84 grams.

• 82 grams.

• 78 grams.

• 76 grams.

• 74 grams.

A z-score tells you...

• the standard deviation of a sampling distribution.

• the original raw score on which it is based.

• if the distribution it comes from is normal.

• how many standard deviations away from the mean a score lies.

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

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 20. Find the z-score of a person who scored 294 on the exam.

• -0.3

• 0.5

• 0.3

• 0.95

On a standardized exam, the scores are normally distributed with a mean of 300 and a standard deviation of 40. Find the z-score of a person who scored 400 on the exam.

• 2.5

• 25

• 2.5%

• -2.5

On a standardized exam, the scores are normally distributed with a mean of 750 and a standard deviation of 100. Find the z-score of a person who scored 580 on the exam.

• -1.7

• 1.7%

• 1.12

• 1.7

On a standardized exam, the scores are normally distributed with a mean of 36 and a standard deviation of 5. Find the z-score of a person who scored 39 on the exam.

• 0.6

• -0.6

• 0.79

• -0.79

On a standardized exam, the scores are normally distributed with a mean of 195 and a standard deviation of 20. Find the z-score of a person who scored 140 on the exam.

• -2.75

• 275

• 2.75

• 5.72

On a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 40. Find the z-score of a person who scored 616 on the exam.

• 2.9

• -2.9

• 29

• 2.99

Which of the following gives the most information about a score in relation to the overall population?

• Raw score

• z score

• Mean