Teresa measures the distance that a traverse system moves an object for a given computer-controlled input pulse. She makes 100 readings, and the mean value is 6.832 m with a sample standard deviation of 1.0 cm. The errors in the measurements are assumed to be random.
a) How many measurements are expected to fall within 0.5 cm of the mean value?
b) How many measurements are expected to fall within 2.0 cm of the mean value?
c) How many measurements are expected to fall within 5.0 cm of the mean value?