Measurements are taken of the thickness of 120 samples of ceramic tiles taken from
a large batch of tiles. The measurements have a mean value of 16.937 mm and a
standard deviation of 0.395 mm. The smallest and largest thickness measurements in
the sample are 16.09 and 17.84 mm. The measurements are divided into 8 data bins
with boundaries at 16.085, 16.305, 16.525, 16.745, 16.965, 17.185, 17.405, 17.625,
and 17.845. The first bin, containing measurements between 16.085 and 16.305, has
6 measurements in it, and the count of measurements in the following successive bins
is 10, 17, 27, 25, 20, 11 and 4. Apply the chi-squared test to see whether the measurements fit a Gaussian distribution to (a) a 95% confidence level and (b) a 97.5%
confidence level.