機率急求過程解答 - Ans.fyi 參考答案

機率急求過程解答

2011-05-18 7:27 pm

The grades of students in a calculus-based probability course are
normal with mean 62 and standard 7. If 90, 80, 70, and 60 are
the respective lowest, A, B, C, and D, what percent of students
in this course get A's, B's, C's, D's and F's?

回答 (1)

0753AVS

2011-05-18 7:46 pm

✔ 最佳答案

Let X be the distribution of the score, X~N(62,7^2)

P( getting A)
=P( X >= 90)
=P(Z>= (90-62)/7 )
=P(Z>=4) ≒ 0

P(getting B or above)
=P( X >= 80)
=P(Z>= (80-62)/7 )
=P(Z>=2.57)
= 1- 0.9949 = 0.0051 = 0.51%

P(getting C or above)
=P( X >= 70)
=P(Z>= (70-62)/7 )
=P(Z>=1.14)
= 1- 0.8729 = 0.1271 = 12.71%

P(getting D or above)
=P( X >= 60)
=P(Z>= (60-62)/7 )
=P(Z>= - 0.29)
= 1- 0.3859 = 0.6141 = 61.41 %

-----------------------------

percentage of A = 0
percentage of B = 0.51%
percentage of C = 12.71% - 0.51% = 12.20%
percentage of D = 61.41% - 12.71 % = 48.70%
percentage of F = 100% - 61.41% = 38.59%

參考: Normal table: http://www.stat.ucla.edu/~ywu/teaching/normal.pdf

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