Question

At an oceanside nuclear power plant, seawater is used as part of the cooling system. this raises the temperature of the water that is discharged back into the ocean. the amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25°


c. what is the standard deviation of the temperature increase?

Answer 1

Answer: 4.33°

Explanation:

The formula to calculate the standard deviation for a uniform distribution for interval [a,b] is given by :-

$\text{Standard deviation}:\sigma=\sqrt{\dfrac{(b-a)^2}{12}}$

Given : The amount that the water temperature is raised has a uniform distribution over the interval = $[10^{\circ},25^{\circ}]$

Then , the standard deviation of the temperature increase is given by :-

$\sigma=\sqrt{\dfrac{(25-10)^2}{12}}\\\\\Rightarrow\sigma=4.33012701892\approx4.33$

Hence, the standard deviation of the temperature increase is 4.33°.