Answer:C) Â [tex]0.58=\dfrac[103-76}{\sigma}[/tex]
Step-by-step explanation:
Given : The distribution of the number of moths captured per night by a certain moth trap is approximately normal with  [tex]\mu=103[/tex].
Also, Â 28 percent of the captures fall below 76 per night, which of the following equation,
On z-table , the z-value corresponding to the p-value of 28% is -0.58.
Since formula for z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex] , where x is random variable and [tex]\sigma[/tex] is standard deviation.
For the current situation, the formula becomes with values  [tex]\mu=103, x=76 , \&\ z=-0.58[/tex] as
[tex]-0.58=\dfrac{76-103}{\sigma}\\\\0.58=\dfrac[103-76}{\sigma}[/tex]
Hence, the equations can be used to find σσ, the standard deviation of the distribution :-
[tex]0.58=\dfrac[103-76}{\sigma}[/tex]
Equation to find the standard deviation of the distribution is;
-0.58 = (76 - 103)/σ
In solving this question, we will make use of z-distribution table and also the z-score formula.
We are given;
Mean; μ = 103
Sample mean; x' = 76
sample percentage; p = 28% = 0.28
From z-score table online, the z-score with a p-value of 0.28 is approximately;
z = -0.58
Now, the formula for z-score is;
z = (x' - μ)/σ
Plugging in the relevant values, we have;
-0.58 = (76 - 103)/σ
Read more at; brainly.com/question/13523179
