For the image uploaded with data, I have following queries:
What is the significance of finding CI Interval, when we already know that we are 95.45% sure about Population Mean will lie in range of (34.6 & 38.6)?
My Question Is, Should Confidence Interval Values (36.40 & 36.79) should have been equal to Range of shaded portion (i.e. 38.6 & 34.6) ???
A 95% confidence interval for the population mean $\mu,$ based on a normal sample of size $n = 100$ with $\bar X = 36.6, S = 2.0,$ would be of the form $\bar X \pm t^* S/\sqrt{n},$ where $t^*$ cuts probability $0.025 =2.5\%$ from the upper tail of Student's t distribution with 99 degrees of freedom.
From printed tables of t distributions or from software (R output below) $t^* = 1.984.$ [Some texts might use approximations, either using the value $1.96$ that cuts probability $0.025$ from the upper tail of a standard normal distribution, or for simplicity just $2.0.]$
Roughly speaking, the desired CI is about $36.6\pm 0.4$ or $(36.2, 37.0).$ Please follow the convention in your textbook, if you need more places of accuracy.
Note: Your figure and the work you have shown in your Question suggests you may be using a "confidence interval" (CI) of the form $\bar X \pm S$ or $\bar X \pm S/\sqrt{n}.$
From a statistical point of view, the first of these variants makes no sense as a CI---its widespread use in some biological and social sciences (to make 'error bars') notwithstanding.
The second of these is approximately a 68% confidence interval.