Mat 143 Statistics Empirical Rule and Z Scores

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%

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 less than 32?

• 81.5%

• 95%

• 97.5%

• 99.7%

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 greater than 36?

• .15%

• 0.30%

• 2.35%

• 0.135%

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

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

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