Determine two consecutive odd integers such that the sum of their squares is a minimum.
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Answer:
Mean is 81%
standard deviation is approximately 4.2%
Step-by-step explanation:
Since the number of boys equals the number of girls, but it is not given, we name it "N". and proceed to calculate the mean as:
Mean = (0.78 * N + 0.84 * N) /(2 N)
using that the total number of students must be N boys + N girls = 2 N
Then the Mean becomes: N *(0.78 + 0.84) /(2 N) = (0.78 + 0.84) / 2 = 1.62 / 2 = 0.81
So the mean is 81%
Now, standard deviation will be calculated by first adding the squares of the deviations: (X-0.81)^2 for the N boys and for the N girls, and then finding the square root of this and finally dividing by the square root of N. That is:
Now finding the square root of this value, and finally dividing it by the square root of N:
which in percent form is: approximately 4.2%