1. Statistics for engineers.

Hello i have a question on statistics.

If you take a random pen, the length is assumed to be a normal distrubution. The expectation-value is 120 mm, and the standard deviation is 20mm.
We take this random pen and use it as a hypotenuse on a right triangle. With one cathethus that is exactly 72mm. Decide an approximation of the expectation-value and the standard devotion for the area of the triangle.

I am stuck and would appreciate some help

2. Well draw it out...

Start off by using the expected length of the hypotenuse together with the Pythagorean theorem. Now, calculate the area. This will be your expected area.

Now, adjust the hypotenuse by a standard deviation and recalculate the area. This will be your area standard deviation.

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Expected Area:

$a^2 + (72)^2 = (120)^2$ Solve for $a.$

$\text{Area}= \frac{1}{2}b h$ Decide what your base and height will be, then calculate.

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