The lengths of two components will be measured several times. The uncertainty in each measurement of the length of the first component is 
=0.02 cm, and the uncertainty in each measurement of the length of the second component is 
=0.08 cm. Let 
denote the average of the measurements of the first component, and let 
denote the average of the measurements of the second component. The total length of the two components will be estimated with the quantity
src="https://sciemce.com/media/4/bb4ad71c08f6dc97xy.jpg" class="w-image" />.
a. Find the uncertainty in the total length if the first component is measured 4 times and the second component is measured 12 times.
b. Find the uncertainty in the total length in terms of n if the first component is measured n times and the second component is measured 16–n times.
c. Determine the best way to allocate 16 measurements between the components by determining the value of n that minimizes the uncertainty.
(a) 
(b) 
(c) The integer value of n than minimizes is 
. Therefore measure the first component 3 times and the second component 13 times.
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src="https://sciemce.com/media/4/bb4ad71c08f6dc97xy.jpg" class="w-image" />.
a. Find the uncertainty in the total length if the first component is measured 4 times and the second component is measured 12 times.
b. Find the uncertainty in the total length in terms of n if the first component is measured n times and the second component is measured 16–n times.
c. Determine the best way to allocate 16 measurements between the components by determining the value of n that minimizes the uncertainty.
(a)
(b)
(c) The integer value of n than minimizes is . Therefore measure the first component 3 times and the second component 13 times.
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