Empirical Rule & Z-Score

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%

Approximately how many juniors scored between 16 and 20 on the ACT?

• 67

• 79

• 13

• 237

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 20 and 28 on the ACT?

• 68

• 475

• 340

• 237

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 greater than a 20 on the ACT?

• 420

• 80

• 340

• 250

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%

Approximately how many students scored between 70 and 80?

• 900

• 100

• 1900

• 950

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 less than 60?

• 32

• 16

• 47

• 50

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 55?

• 16%

• 2.35%

• 2.5%

• 0.15%

At a local high school, GPA's are normally distributed. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%