a) Find the lowest scores for grade A
b) Find the range of the scores for B
更新1:
ans of (b) is 15
dispersion(2)
2011-06-12 7:20 am
In a Chinese Language examination, the top 2.5%of the scores are given grade A, the next 13.5% are given grade B, then the next 16% are given grade C, and the rest are given grade D to F. It is known that the scores are normally distributed, and the mean and standard deviation of the scores are 60 and 15 respectively.
a) Find the lowest scores for grade A
b) Find the range of the scores for B
a) Find the lowest scores for grade A
b) Find the range of the scores for B
回答 (3)
2011-06-12 8:00 am
✔ 最佳答案
a) The lowest scores for grade A
=μ+2σ
= 60 + 15 * 2
=90
b)
μ+σ < the scores for B < μ+2σ
75 < the scores for B < 90
2011-06-15 01:11:03 補充：
So, range = 90 - 75 = 15
2011-06-12 6:54 pm
89.4 - 74.925 = 14.475
2011-06-12 2:06 pm
a) top 2.5% => bottom 97.5%
the z-value for 0.975 is 1.96
Hence the required lowest scores for grade A
= μ+1.96σ
= 60 + 1.96 * 15
= 89.4
b) A and B students => top 16% => bottom 84%
the z-value for 0.84 is 0.995
The lowest scores for grade B
= μ+ 0.995σ
= 60+ 0.995 * 15 = 74.925
Hence the range required is [74.925, 89.4]
the z-value for 0.975 is 1.96
Hence the required lowest scores for grade A
= μ+1.96σ
= 60 + 1.96 * 15
= 89.4
b) A and B students => top 16% => bottom 84%
the z-value for 0.84 is 0.995
The lowest scores for grade B
= μ+ 0.995σ
= 60+ 0.995 * 15 = 74.925
Hence the range required is [74.925, 89.4]
參考: Normal Table
收錄日期: 2021-04-20 00:47:17
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110611000051KK01313