Empirical Rule & Z-Score

In a normal distribution, what percent of the values lie above the mean?

• 13.5%

• 34%

• 50%

• 68%

In a normal distribution, what percent of the values lie within one standard deviation of the mean?

(from z = -1 to z = 1)

• 13.5%

• 34%

• 95%

• 68%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

What percent of scores are between 65 and 75?

• 34%

• 50%

• 68%

• 81.5%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

What percent of scores are less than 70?

• 34%

• 50%

• 16%

• 84%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

What percent of scores are greater than 75?

• 2.35%

• 2.5%

• 16%

• 13.5%

2000 freshmen at State Univ. took a Biology test. The scores were distributed normally with μ=70 and σ=5.

Approximately how many students scored between 60 and 80?

• 95

• 100

• 1900

• 1950

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score is 3 standard deviations below the mean?

• 12

• 16

• 20

• 21

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What ACT score has a z-score of 1?

• 20

• 24

• 25

• 28

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What percent of ACT scores are between 20 and 28?

• 34%

• 68%

• 81.5%

• 95%

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4.

What percent of ACT scores are between 16 and 24?

• 34%

• 47.5%

• 49.85%

• 50%