Answer :
M = 135
Step by Step Explanation :
See the photo attached :) it’s kinda hard to explain in words but you cancel out the 36.50 by subtracting it on both sides, and then the equation becomes 13.50 = 0.10m. Since we have to get the m by itself, you cancel out the 0.10 by subtracting on both sides, and it leaves you with 135 = m
(Ignore my messy handwriting on a post it :3)
I hope this helped! If u have any questions feel free to comment on this!
Answer:
A sample size of at least 737 specimens is required.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so 
Now, find the width M as such

In which
is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:

So:





A sample size of at least 737 specimens is required.
If you are in college, this question is likely done with calculus.
a = 12
k = 0.2
v(x) = 0 at the maximum after differentiation
V(x) = kx(a - x)
The easiest way to do this is to remove the brackets.
V(x) = akx - kx^2 Substitute the constants
V(x) = 12*0.2*x - 0.2x^2
V(x)/dx = 2.4 - 0.4x = 0 at the maximum
2.4 - 0.4x = 0
0.4x = 2.4
x = 2.4/0.4
x = 6
If you don't know any calculus yet, you can do this by completing the square.