group of 300 professionals sat for a competitive exam. The results show the information of
marks obtained by them have a mean of 60 and a standard deviation of 12. The pattern of marks follows a
normal distribution. Answer the following questions.
A. What is the percentage of students who score more than 80.
B. What is the percentage of students who score less than 50.
C. What should be the distinction mark if the highest 10% of students are to be awarded distinction?
Answers
Given: 300 professionals sat for a competitive exam
Mean = 60 SD = 12
SD =standard deviation
To Find : percentage of students who score more than 80.
percentage of students who score less than 50.
distinction mark if the highest 10% of students are to be awarded distinction
Solution:
Z score = (Value - Mean)/SD
Z score for 80 %
= (80 - 60)/12
= 20/12
= 1.667
percentage of students who score more than 80. = ( 100 - 95.23) = 4.67 %
Z score for 50 %
= (50 - 60)/12
= -10/12
= -0.833
percentage of students who score less than 50 = 20.25 %
highest 10% of students
=> 90 % students no distinction
z score for 90% = 1.282
1.282 = (Value - 60)/12
=> value = 75.384
Hence distinction mark = 75.384
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