Scores on a quiz were normally distributed and had a mean of 10 and standard deviation of 3. For each of the following scores, find the


% Area Above  % Area Below 
5  
6  
7  
8  
9  
11  
12  
14  
15  
16  
18 
To find:
The
Solution:
The
% Area Above  % Area Below  
5  95.25  4.75  
6  90.82  9.18  
7  84.13  15.87  
8  74.86  25.14  
9  62.93  37.07  
11  37.07  62.93  
12  25.14  74.86  
14  9.18  90.82  
15  4.75  95.25  
16  2.28  97.72  
18  0.38  99.62 
Given:
The scores of the quiz are normally distributed with a mean of 10 and standard deviation of 3.
The scores of the quiz are
Description:
The normal curve is symmetrical and its mean is equal to the median. The area below and above the mean is 50% or 0.05.
Formula used:
Let the data values be denoted by
The formula to calculate the
Where,
Calculation:
Given that the mean is 10 and standard deviation is 3.
For the score of 5,
Substitute 5 for
From the normal distribution table the area below the score of
The area between the mean and the score
Use the concept of symmetry, the area above the score of
The percentage of area below and above the score of
For the score of 6,
Substitute 6 for
From the normal distribution table the area below the score of
The area between the mean and the score
Use the concept of symmetry, the area above the score of
The percentage of area below and above the score of
For the score of 7,
Substitute 7 for
From the normal distribution table the area below the score of
The area between the mean and the score
Use the concept of symmetry, the area above the score of
The percentage of area below and above the score of
For the score of 8,
Substitute 8 for
From the normal distribution table the area below the score of
The area between the mean and the score
Use the concept of symmetry, the area above the score of
The percentage of area below and above the score of
For the score of 9,
Substitute 9 for
From the normal distribution table the area below the score of
The area between the mean and the score
Use the concept of symmetry, the area above the score of
The percentage of area below and above the score of
For the score of 11,
Substitute 11 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
For the score of 12,
Substitute 12 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
For the score of 14,
Substitute 14 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
For the score of 15,
Substitute 15 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
For the score of 16,
Substitute 16 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
For the score of 18,
Substitute 18 for
From the normal distribution table the area above the score of
The area between the mean and the score
Use the concept of symmetry, the area below the score of
The percentage of area above and below the score of
Conclusion:
Therefore, the
% Area Above  % Area Below  
5  95.25  4.75  
6  90.82  9.18  
7  84.13  15.87  
8  74.86  25.14  
9  62.93  37.07  
11  37.07  62.93  
12  25.14  74.86  
14  9.18  90.82  
15  4.75  95.25  
16  2.28  97.72  
18  0.38  99.62 
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