Question

Hello,

Please find attached the question I would like help on. Specifically part b.

I have already figured out the answer to part a is 1/2 and I think if I can figure out part b, I can do part c.

Step 1

a)

Total area under the curve is a triangle with area = 1/2 * base * height = 1/2 * 4 * C = 2C

Since you've figured out part a), you must already know that the total area under the density curve = 1

Therefore, 2C = 1 which gives us C=1/2

Step 2

b)

P(x<=1) means percent of area under the density curve which is less than or equal to 1 as shown by yellow triangle.

To calculate the area of the yellow traingle, we need its height which can be calculated by splitting the total areas into 3 parts.

Step 3

Area of region I = 1/2 * (1-0)* x = 0.5x

Area of region 2 = (4-1)*x = 3x

Area of region 3 = 1/2 *(4-1)*(0.5-x) = 0.75-1.5x

Sum of all three areas must be equal to 1

Therefore, 0.5 x + 3 x + 0.75 -1.5x =1 or

&nbs...

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