Question

A student needs to accurately deliver 30 mL of solution but has only a 10 mL pipet. From a prior calibration, the student knows that a 95% confidence interval for a single delivery from this pipet is 9.9914 ± 0.0077 mL. [Note that “accurately deliver” does not mean to pipet exactly 30 mL. The actual volume just needs to be near 30 mL and accurately known: “the exact amount doesn’t matter as long as you know exactly how much it is.”] The student decides to use three deliveries from the 10 mL pipet. Why is it safe to assume that the random errors in these deliveries are uncorrelated? Calculate a 95% confidence interval for the total volume.

Answer 1

Here we are repeating the measurement of the same quantity (10 mL) three times to deliever 30 mL of the solution. Hence the value of random error for the three different measurement for the same quantity will be different. Hence the value of random error for these three deliveries will be inconsistance and are uncorrelated.

At 95% confidence level 95% of the measurements will lie in the given range 9.9914 ± 0.0077 mL.

Hence a 95% confidence interval for the total volume = 3 x (9.9914 ± 0.0077) mL = 29.974 +/- 0.023 mL