SECTION 3.25513. (a) The uncertainty in the average of 9 measurements is approximately equal tos90 081 30 027 cm.(b) The uncertainty in a single measurement is approximately equal tos, which is 0.081 cm.15. (a) LetX87 0 denote the average of the eight measurements, lets2 0 denote the sample standard deviation,and letσdenote the unknown population standard deviation. The volume is estimated withX. The uncertaintyisσXσ8s82 080 7 mL.(b)σXs162 0160 5 mL(c) Letnbe the required number of measurements. Thenσn0 4.Approximatingσwiths2 0 yields 2 0n0 4, son25.17.LetXdenote the average of the 10 yields at 65 C, and letYdenote the average of the 10 yields at 80 C. LetsXdenote the sample standard deviation of the 10 yields at 65 C, and letsYdenote the sample standard deviationof the 10 yields at 80 C. ThenX70 14,
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