Chapter 6.2, Problem 55E

To determine

To find: The mean and standard deviation of the difference between the readings.

Answer to Problem 55E

The mean and standard deviation are 0.001 and 0.002236.

Explanation of Solution

Given:

For X:

Population mean $\left(\mu \right)=2.000$

Population standard deviation $\left(\sigma \right)=0.002$

For Y:

Population mean $\left(\mu \right)=2.001105$

Population standard deviation $\left(\sigma \right)=0.001$

Calculation:

The mean value and standard deviation of the difference between Y and X can be computed as:

  $\begin{array}{c}{\mu }_{Y-X}={\mu }_Y-{\mu }_X\\ =2.001-2.000\\ =0.001\end{array}$

The average difference between the Y and X is expected to be 0.001.

  $\begin{array}{c}{\sigma }_{Y-X}=\sqrt{{\sigma }^2{}_Y-{\sigma }^2{}_X}\\ =\sqrt{{0.001}^2+{0.002}^2}\\ =\sqrt{0.000005}\\ =0.002236\end{array}$

The difference that exists between the two readings on an average is expected to be 0.001 g and it differs on average of 0.002236 g.