Independent solution

How to solve this Uniform Distribution question

Setup

Setup

Let X be the base amount and express the total charge Y as an affine transformation.

X∼Uniform⁡(100,225)X\sim\operatorname{Uniform}(100,225)
Y=1.30X+15Y=1.30X+15

Model

Model

A uniform interval's standard deviation is its width divided by the square root of twelve. Under an affine transformation, constants do not affect standard deviation and a positive multiplier scales it directly.

SD⁡(X)=225−10012\operatorname{SD}(X)=\frac{225-100}{\sqrt{12}}
SD⁡(Y)=1.30SD⁡(X)\operatorname{SD}(Y)=1.30\operatorname{SD}(X)

Compute

Compute

Substitute the interval width and surcharge factor.

SD⁡(Y)=1.30(12512)\operatorname{SD}(Y)=1.30\left(\frac{125}{\sqrt{12}}\right)
SD⁡(Y)=46.90970937\operatorname{SD}(Y)=46.90970937

Answer

Answer

The total-charge standard deviation rounds to 46.9.

46.9(D)\boxed{46.9\quad\text{(D)}}