For any number n, if n2 is even, then n must be even. This means n being even is a condition for n2 being even.

For any number n, if n2 is even, then n must be even. This means n being even is a Necessary condition for n2 being even.

Step-by-step explanation:

Necessary Condition:-A condition that says that the result has to be true but does not guarantee any kind of result.

Suppose we  assume that n is not even (i.e., it is odd)  

and show that n^2 is not even (i.e., it is odd).

n is odd then  you can write

   n = 2*k + 1 for an  integer k.

Then,  

  n^2 = 4*k^2 + 4*k + 1  

      = 2 * (2*k^2 + 2*k) + 1  

which is clearly odd.  

This completes the proof that for any number n, if n2 is even, then n must be even

No.

Step-by-step explanation:

According to the central limit theorem,

Then the distribution of sample means can be approximated by a normal distribution. And the mean of this distribution converges true mean of annual incomes.

But distribution of annual incomes inside a sample may not be normal.