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Chapter 6: Q.55 (page 380)

A balanced scale You have two scales for measuring weights in a chemistry lab. Both scales give answers that vary a bit in repeated weighings of the same item. If the true weight of a compound is 2.00grams (g), the first scale produces readings Xthat have mean 2.000gand standard deviation 0.002g. The second scale’s readings Yhave mean 2.001gand standard deviation . 0.001gThe readingsXandYare independent. Find the mean and standard deviation of the difference Y-Xbetween the readings. Interpret each value in context.

Short Answer

Expert verified

The difference between the readings is on average μY-X=0.001g,which varies on about σY-X≈0.002236g.

Step by step solution

01

Given Information

Given in the question that:

μX=2.000

σX=0.002

μY=2.001

σY=0.001

We have to find out that the mean and standard deviation of the difference Y-Xbetween the readings.

02

Explanation

The property mean and variance (ifXand Yare independent):

μX+Y=μX+μYσ2X+Y=μ2X+μ2Y

Then we obtain:

μY-X=μY-μX=2.001-2.000=0.001

σ2Y-X=μ2Y+μ2X=0.0012+0.0022=0.000005

The standard deviation is the square root of the variance:

σY-X=σ2Y-X=0.000005≈0.002236

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