How is the brain organized, and what do its higher structures do?
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Yaya says:
IQ Scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?
IQ Scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of IQ scores are between 70 and 130?
<span>Solution: </span>130 – 100 = 30 which is 2(15). Thus, 130 is 2 standard deviations to the right of the mean. 100 – 70 = 30 which is 2(15). Thus, 70 is 2 standard deviations to the left of the mean. Since 70 to 130 is within 2 standard deviations of the mean, we know that <span>about 95% of the IQ scores would be between 70 and 130.</span>
Answer:
The sum of the area of the shaded regions = 0.248685
Explanation:
The sum of the area of the shaded region is given as follows;
The point of intersection of the graphs are;
y = x/2
y = sin²x
∴ At the intersection, x/2 = sin²x
sinx = √(x/2)
Using Microsoft Excel, or Wolfram Alpha, we have that the possible solutions to the above equation are;
x = 0, x ≈ 0.55 or x ≈ 1.85
The area under the line y = x/2, between the points x = 0 and x ≈ 0.55, A₁, is given as follows
1/2 × (0.55)×0.55/2 ≈ 0.075625
The area under the line y = sin²x, between the points x = 0 and x ≈ 0.55, A₂, is given using as follows;
Therefore;
∴ A₂ =1/2 × ((0.55 - sin(0.55)×cos(0.55)) - (0 - sin(0)×cos(0)) ≈ 0.0522
The shaded area, = A₁ - A₂ = 0.075625 - 0.0522 ≈ 0.023425
Similarly, we have, between points 0.55 and 1.85
A₃ = 1/2 × (1.85 - 0.55) × 1/2 × (1.85 - 0.55) + (1.85 - 0.55) × 0.55/2 = 0.78
For y = sin²x, we have;
The shaded area, = A₄ - A₃ = 1.00526 - 0.78 ≈ 0.22526
The sum of the area of the shaded regions, ∑A = +
∴ A = 0.023425 + 0.22526 = 0.248685
The sum of the area of the shaded regions, ∑A = 0.248685