WorksheetsCh.5- Empirical Rule and Z-Scores
Total questions: 22
Worksheet time: 21mins
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%
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%
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%
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
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%
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 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%
