PSY 3200
PSY 3200 系列
Unit #3 AS: Calculating Percentages
单元 #3 AS：计算百分比
You will be given a series of questions regarding a normal distribution, you will be asked to either determine the percentage above or below particular raw scores; or to calculate the raw score that will correspond to a particular percentage.
您将被问到一系列关于正态分布的问题，您将被要求确定高于或低于特定原始分数的百分比;或计算对应于特定百分比的原始分数。
You will be asked to calculate either raw scores or percentages. For each question write out your calculation, the appropriate Z score, what on the curve you should be shading, the exact percentage from the normal curve table and the final answer. Type this all out on the assigned word document and submit via blackboard.
您将被要求计算原始分数或百分比。对于每个问题，请写出您的计算结果、适当的 Z 分数、您应该在曲线上着色的内容、正常曲线表的确切百分比以及最终答案。在分配的 word 文档上输入所有内容并通过 blackboard 提交。
A group of students take a Statistics Exam where the average was M = 90 and the standard deviation was SD = 7.8. Answer the following questions regarding this distribution using your normal curve table. Depending on the problem, be sure to identify the raw scores, Z scores, what in particular you shaded when creating a curve and the final answer. (5 pts each)
一组学生参加统计考试，平均分是 M = 90，标准差是 SD = 7.8。使用正态曲线表回答以下有关此分布的问题。根据问题的不同，请务必确定原始分数、Z 分数、 创建曲线时特别着色的内容以及最终答案。（各 5 分）
1. If you score a 99, what percentage of the population scored above you?
1. 如果你得了 99 分，那么得分高于你的人口百分比是多少？
12.51%
99-90 = 9/7.8 = 1.15
Z score = 1.15
Z 分数 = 1.15
Percentage from normal curve = 37.49%
与正态曲线的百分比 = 37.49%
Scored above = 12.51%
以上得分 = 12.51%
2. What raw score is needed to be in the top 8%?
2. 进入前 8% 需要什么原始分数？
100.998
X= (1.41)(7.8) + 90 = 100.998
X = （1.41）（7.8） + 90 = 100.998
Raw score = 100.998
原始分数 = 100.998
Z score = 1.41
Z 分数 = 1.41
Shaded area = above 100.98
阴影区域 = 高于 100.98
3. What raw score is needed to reach the 14th percentile?
3. 需要什么原始分数才能达到第 14 个百分位？
81.576
X = (-1.08)(7.8) +90 = 81.576
X = （-1.08）（7.8） +90 = 81.576
Raw score = 81.576
原始分数 = 81.576
Z score = -1.08
Z 分数 = -1.08
Shade area = above 81.576
阴影区域 = 81.576 以上
4. What range of raw scores makes up the middle 40%?
4. 中间 40% 的原始分数范围是多少？
85.944-94.056
85.944-94.056
X1=(.52)(7.8) + 90 = 94.056
X1=（.52）（7.8） + 90 = 94.056
X2=(-.52)(7.8)+90=85.944
X2=（-.52）（7.8）+90=85.944
5. If you score an 80, what percentage of the population scored above you?
5. 如果你得了 80 分，那么得分高于你的人口中有多少百分比？
89.97%
80-90 = -10/7.8=-1.28
Z score = -1.28
Z 分数 = -1.28
Percentage from normal curve = 39.97
与正态曲线的百分比 = 39.97
Because it is a negative value - 10.03% scored below,
因为它是一个负值 - 10.03% 的分数低于 10.03%，
therefore,
因此
Score above = 89.97%
以上分数 = 89.97%
6. What percentage of the population lands between the raw scores of 82 and 107?
6. 有多少百分比的人口介于 82 和 107 的原始分数之间？
83.11%
82-90/7.8 = -1.02 107-90/7.8 = 2.17
Z scores = 1.02 and 2.17
Z 分数 = 1.02 和 2.17
15.39 in tail and 1.5 in tail = 16.89
15.39 英寸尾部和 1.5 英寸尾部 = 16.89
100-16.89 = 83.11%
7. If you score a 85, what percentage of the population scored above you?
7. 如果你得了 85 分，那么得分高于你的人口百分比是多少？
73.89
85-90/7.8 = -.64 = 26.11
Z score = .64
Z 分数 = .64
Percentage from normal curve - 23.89%
正常曲线的百分比 - 23.89%
100-26.11 = 73.89
Scored above = 73.89
以上得分 = 73.89
8. What raw score is needed to be in the bottom 16%?
8. 需要多少原始分数才能进入后 16%？
82.278
(-.99)(7.8) + 90 = 82.278
（-.99）（7.8） + 90 = 82.278
Z score = .99
Z 分数 = .99
% in tail = 16.11
尾部百分比 = 16.11
Shade area - below 82.278
阴影区域 - 低于 82.278
9.If you score a 96, what percentage of the population scored above you?
9.如果你得了 96 分，那么得分高于你的人口百分比是多少？
22.36
96-90/7.8 = 0.76
Z score = 0.76
Z 分数 = 0.76
Percentage from normal curve = 27.64%
与正态曲线的百分比 = 27.64%
Score above = 22.36%
以上分数 = 22.36%
10. What raw score is needed to be in the top 17%?
10. 进入前 17% 需要什么原始分数？
97.41
(.95)(7.8) + 90 = 97.41
（.95）（7.8） + 90 = 97.41
Z score = .95
Z 分数 = .95
% in tail = 17.11
尾部百分比 = 17.11
Shade area - above 97.41
阴影区域 - 97.41 以上
11. What raw score is needed to reach the 90th percentile?
11. 需要什么原始分数才能达到第 90 个百分位？
99.984
Tail % = 10.03
尾部 % = 10.03
(1.28)(7.8) + 90 = 99.984
（1.28）（7.8） + 90 = 99.984
Z Score = 1.28
Z 分数 = 1.28
Shade area - above 99.984
阴影面积 - 99.984 以上
12. What percentage of the population lands between the raw scores of 83 and 100?
12. 原始分数介于 83 到 100 之间的人口百分比是多少？
71.3%
83-90/7.8 = -0.89
100-90/7.8 = 1.28
18.67% + 10.03% = 28.7
100-38.7 = 71.3%
13. If you score a 85, what percentage of the population below you?
13. 如果你得了 85 分，那么低于你的人口中有多少百分比？
26.11
85-90/7.8 = -.64 = 26.11
Z score = .64
Z 分数 = .64
Percentage from normal curve - 23.89%
正常曲线的百分比 - 23.89%
Scored above = 26.11
以上得分 =26.11
14. What raw score is needed to be in the bottom 28%?
14. 需要多少原始分数才能进入后 28%？
85.476
Z score = -.58
Z 分数 = -.58
(-.58)(7.8) + 90 = 85.476
（-.58）（7.8） + 90 = 85.476
Percentage from normal curve = 21.90
与正态曲线的百分比 = 21.90
15. What percentage of the population lands between the raw scores of 86 and 105?
15. 有多少百分比的人口介于 86 到 105 的原始分数之间？
66.76%
86-90/7.8 = -0.51
Percentage from normal curve – 19.5%
正常曲线的百分比 – 19.5%
105-90/7.8 = 1.92
Percentage from normal curve – 47.26%
正常曲线的百分比 – 47.26%
19.5% + 47.26%=66.76%