Question

A sample is taken from a batch of stainless steel weights that are manufactured in the shape of solid cylinders. The height, h, and radius, r, are recorded for each weight in the sample as follows:

Height h/cm	Radius r/cm
10.02	4.01
9.93	4.03
9.91	3.96
10.03	3.99
10.05	3.99
9.99	4.03

The density of the stainless steel used is 7.958 × 10^–3 kg cm^–3.

a. Use this data set to calculate the mean, standard deviation, and standard uncertainty for the height and for the radius of the sample. Hence write the height and radius for the sample, including the uncertainties in each.

b. Calculate the mean mass for the sample and the resultant uncertainty. State the mean mass including its uncertainty in kg.

c. The batch of weights is required to have a mass of 4.02 kg with a tolerance ± 0.01kg. Use your result for the mass and its uncertainty to decide if the sample is within tolerance.

Answer 1