Empirical Rule and Z-Score

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%

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 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%

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

Approximately how many juniors scored between 12 and 20 on the ACT?

• 67

• 79

• 100

• 180

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 24 and 28?

• 15%

• 13.5%

• 34%

• 47.5%

500 juniors at Central High School took the ACT last year. The scores were distributed normally with μ=24 and σ=4. Approximately how many juniors scored between 16 and 20 on the ACT?

• 67

• 79

• 13

• 237

Approximately how many juniors scored between 20 and 28 on the ACT?

• 68

• 475

• 340

• 237

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 60?

• 97.5%

• 47.5%

• 95%

• 81.5%