In a sample of 1000 cases, the mean of a certain test is 14 and s.d. is 2.5. assuming the distribution to be normal, find(a) how many students score between 12 and 15?(b) how many score above 18?(c) how many score below 8?(d) how many score 16?
Answers
Given : in a sample of 1000 cases, the mean of a certain test is 14 and standard deviation = 2.50.
To Find : Assuming normality distribution,
a) how many individuals score between 12 and 15
b) how many score above 18?
(c) how many score below 8?
Solution:
Mean = 14
SD = 2.5
Z score = ( Value - Mean)/SD
Z score for 12
= ( 12 - 14)/2.5
= -0.8
for -0.8 z score = 0.2119
Z score for 15
= ( 15 - 14)/2.5
= 0. 4
for 0.4 z score = 0.6554
between 12 and 15 = 0.6554 - 0.2119
= 0.4435
Sample of 1000 Hence 1000 x 0.4435 = 443.5 = 444
444 people between 12 and 15
score above 18
Z score for 18
= ( 18 - 14)/2.5
= 1. 6
for 1.6 z score = 0.9452
Above 18 = 1 - 0.9452 = 0.0548
1000 x 0.0548 = 54.8 = 55
55 scores above 18
score below 8
Z score for 8
= (8 - 14)/2.5
= -2.4
for -2.4 z score = 0.0082
1000 x 0.0082 = 8.2 = 8
8 scores below 8
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