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Answer:
a. 72
b. 816
c. 570
d. 30
Step-by-step explanation:
Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.
Please refer the figure for a better understanding.
a. In a normal distribution, Mean = Median = Mode
Therefore, Median = Mean = 72
b. We have to know that 68% of the values are within the first standard deviation of the mean.
i.e., 68% values are between Mean Standard Deviation (SD).
Scores between 63 and 81 :
Note that 72 - 9 = 63 and
72 + 9 = 81
This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.
Now, Scores between 63 and 81 =
= 68 X 12 = 816.
That means 816 students have scored between 63 and 81.
c. We have to know that 95% of the values lie between second Standard Deviation of the mean.
i.e., 95% values are between Mean 2(SD).
Note that 90 = 72 + 2(9) = 72 + 18
Also, 54 = 63 - 18.
Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to of the values.
Therefore, Scores between 72 and 90 =
= 570.
That is a total of 570 students scored between 72 and 90.
d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.
In this case, 5 % of the values lie between below 54 and above 90.
Since, we are asked to find scores below 54. It should be 2.5% of the values.
So, Scores below 54 =
= 2.5 X 12 = 30.
That is, 30 students have scored below 54.
