PROBLEMS
Q19. The marks obtained in mathematics by 1000 students is normally distributed with mean 78% and stan-
dard deviation 11%. Determine
(i) How many students got marks above 90%
(ii) What was the highest mark obtained by the lowest 10% of the student
(iii) Within what limits did the middle of 90% of the students lie.
Answers
23 students got marks above 90% ,Middle of 90% of the students lie between 60 % to 96 %
Step-by-step explanation:
Mean = 78 %
SD = 11 %
Value = 90 %
Z = (Value - Mean)/SD
=> Z = (90 - 78)/11 = 2
for Z = 2 value is 0.9772
students got marks above 90% = 1000 * ( 1 - 0.9772) ≈ 23
23 Students got marks above 90 %
highest mark obtained by the lowest 10% of the student
=> Z = -1.28
-1.28 = (value - 78 )/11
=> Value = 63.92 ≈ 64
highest mark obtained by the lowest 10% of the student = 64 %
middle of 90% of the students lie
=> 5% to 95 % students
=> z = -1.645 & z = 1.645
-1.645 = (value - 78 )/11 => Value = 59.9 ≈ 60
1.645 = (value - 78 )/11 => Value = 96.1 ≈ 96
middle of 90% of the students lie between 60 % to 96 %
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