Answer:
c) 2
d) 0.96
Step-by-step explanation:
We are given the following in the question:

a) probability density function.
![\displaystyle\int^{\infty}_{\infty}f(x) dx = 1\\\\\displaystyle\int^{\infty}_{-\infty}2x^{-3}dx = 1\\\\\displaystyle\int^{\infty}_{1}2x^{-3}dx\\\\\Rightarrow \big[-x^{-2}\big]^{\infty}_1\\\\\Rightarrow -(0-1) = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B%5Cinfty%7Df%28x%29%20dx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D2x%5E%7B-3%7Ddx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B1%7D2x%5E%7B-3%7Ddx%5C%5C%5C%5C%5CRightarrow%20%5Cbig%5B-x%5E%7B-2%7D%5Cbig%5D%5E%7B%5Cinfty%7D_1%5C%5C%5C%5C%5CRightarrow%20-%280-1%29%20%3D%201)
Thus, it is a probability density function.
b) cumulative distribution function.

c) mean of the distribution

d) probability that the size of random particle will be less than 5 micrometers

Answer:
432 ft²
Step-by-step explanation:
The formula of finding the area of a trapezoid: (base 1 + base 2/ 2) x h
(base 1 + base 2/ 2) x h
= (20 + 28/2) x 18
= 24 x 18
= 432 ft²
56 is equal to the product of 7 and 8 hope it helps!
I believe the answer you're looking for is <span>0.9836</span>