Tasha's bedroom is shaped like a square. The room has an area of 169 ft?.
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Well, check the picture below, that's a triangular prism
so.. if you notice, is really just 2 triangles and 3 rectangles stacked up to each other at the edges
so.. if you just find the area of the 3 rectangles, and the two triangles, sum all five areas up, and you're golden
in your picture, notice the tickmarks, that triangle has all sides equal to each other, so.. if one is 6 units, so are the other sides as well
now.. to get the area of a triangle is 1/2bh as you'd know... so.. what the dickens is the "h" or height of the triangle anyway, well
that's the altitude or height, you already know the base, notice the tickmark
so, get the area of those 2 triangles, and the 3 rectangles and sum them up, and that's the surface area of the triangular prism
so.. if you notice, is really just 2 triangles and 3 rectangles stacked up to each other at the edges
so.. if you just find the area of the 3 rectangles, and the two triangles, sum all five areas up, and you're golden
in your picture, notice the tickmarks, that triangle has all sides equal to each other, so.. if one is 6 units, so are the other sides as well
now.. to get the area of a triangle is 1/2bh as you'd know... so.. what the dickens is the "h" or height of the triangle anyway, well
that's the altitude or height, you already know the base, notice the tickmark
so, get the area of those 2 triangles, and the 3 rectangles and sum them up, and that's the surface area of the triangular prism
We have
425 corresponds to a z of
575 corresponds to
So we want the area of the standard Gaussian between -3/4 and 3/4.
We look up z in the standard normal table, the one that starts with 0 at z=0 and increases. That's the integral from 0 to z of the standard Gaussian.
For z=0.75 we get p=0.2734. So the probability, which is the integral from -3/4 to 3/4, is double that, 0.5468.
Answer: 55%