Standard Deviation and Distribution

On a standardized exam, the scores are normally distributed with a mean of 48 and a standard deviation of 5. Find the z-score of a person who scored 38 on the exam.

• -1

• -2

• -3

• 0

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

• 0

• 1

• 2

• -1

Based on the normal distribution curve in the picture, what is the mean and the standard deviation of the data?

• 50 and 5

• 50 and -5

• 55 and 5

• 55 and -5

Standard deviation tells us...

• the spread of the data

• the average of the data

• the range of the data

When Avani goes bowling, her scores are normally distributed with a mean of 145 and a standard deviation of 12. Using the empirical rule, determine the interval that would represent the middle 68% of the scores of all the games that Avani bowls.

When Julia goes bowling, her scores are normally distributed with a mean of 200 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Julia bowls does she score between 158 and 242?

In a certain population, the mean score on a test is 420. The standard deviation is 105. If the distribution of scores is normal, which of these scores should occur most often?

• 526

• 540

• 314

• 385

A set of scores with a normal distribution has a mean of 32 and a standard deviation of 3.7. Which score could be expected to occur the least often?

• 40

• 36

• 29

• 26

Liz has applied to a college that requires students to score in the top 6.7% on the math portion of an aptitude test. The scores on the test are approximately normally distributed with a mean score of 576 and a standard deviation of 104. What is the minimum score Lix must earn to meet the requirement

• 680

• 740

• 732

• 784

According to the empirical rule, how much of the data falls within 3 standard deviations? 

• 25%

• 68%

• 95%

• 99.7%