Empirical Rule & Z-Score

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3?

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

According to the empirical rule, what percentage of data falls within 1 standard deviation of the mean?

• 25%

• 68%

• 95%

• 99.7%

The z-score represents.....

• the amount of standard deviations a data value is above or below the mean.

• the percentile the data value is above or below the mean.

• the amount of standard deviations a data value is above or below the median.

• the percent the data value is above or below the mean.

μ = 70 , σ = 8 , X (given value) = 50 . Find z score

• 2.5

• -2.5

• 5.2

• -5.2

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

In a normal distribution, what percent of the values lie within three standard deviations of the mean?

(from z = -3 to z = 3)

• 99.7%

• 81.5%

• 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 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 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%