Answer:
Part (A) The required PMF is: 
Part (B) 
Step-by-step explanation:
Consider the provided information.
There are 50 industrial rms. An inspector will visit 10 randomly selected rms to check for violations of regulations.
Part (A)
15 of the rms are actually violating at least one regulation.
Let X is the number of firms violate at least one regulation from 10 randomly selected rms to check for violations of regulations out of 50 firms of which 15 5 of the rms are actually violating.
Therefore, 
We need to determine probability mass function.
Hence, the required PMF is:
Part (B) If there are 500 rms in the area, of which 150 are in violation, approximate the pmf of part.
Here N=500 so find the probability of p as shown below:
and n=10
The following information will help us with this problem:
![\sqrt[m]{x^n} = x^{\frac{n}{m}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%5En%7D%20%3D%20x%5E%7B%5Cfrac%7Bn%7D%7Bm%7D)
When we use that information in the context of this problem, we can find:
![\sqrt[4]{15^7} = 15^{\frac{7}{4}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B15%5E7%7D%20%3D%2015%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D)
Thus, a = 15, b = 7, and c = 4.
So first you subtract 2001-1682=319.
There is just 1 step, and it is hard to show work here.
Hope this helped! :)
<span>We can analyze the four optons. 1) Option A. A parallelogram with all four angles of the same measure can be either a square or a rectangle, then this option is not valid. 2) Optrion B. gives not information. 3) A rhombus (a diamond) is a parallelogram with four congruent side (square is a specific case of rhmbus but not all rhombus are squares), and it is enouh to say that one diagonal bisects two interior angles, to conclude that it is a rhombus. 4) If a diagonal creates congruent angles, but you do not know what happens with the opposed angle, you cannot conclude that the parallelogram is a rectangle; it could be a trapezoid with one side perpendicular to the parallel sides. By t his analysis, the answer is option C.</span>
