Independent solution

How to solve this Moments question

Setup

Setup

Expand the centered expression so that the unknown first moment appears.

E⁡[(X−1)2]=E⁡[X2]−2E⁡[X]+1\operatorname{E}[(X-1)^2]=\operatorname{E}[X^2]-2\operatorname{E}[X]+1

Model

Model

Insert the two supplied second-moment values and solve for the mean.

47=61−2E⁡[X]+147=61-2\operatorname{E}[X]+1
E⁡[X]=61+1−472=7.5\operatorname{E}[X]=\frac{61+1-47}{2}=7.5

Compute

Compute

Convert the raw second moment to variance and take its positive square root.

Var⁡(X)=61−7.52=4.75\operatorname{Var}(X)=61-7.5^2=4.75
SD⁡(X)=4.75=2.1794495\operatorname{SD}(X)=\sqrt{4.75}=2.1794495

Answer

Answer

The standard deviation rounds to 2.18.

2.18(A)\boxed{2.18\quad\text{(A)}}