Question

The heights of 3 million Americans was measured, and the data was found to be (approximately) Normally distributed. The average height (mean) was approximately 170 cm and the standard deviation approximately 12 cm. Why is there approximately 0% chance that someone weighs exactly 180 cm? Assume that you could measure someone perfectly .

Answer 1

Let X denote the height measurement of 3 million Americans the X  is  normally distributed and the average height was approximately 170 cm and the standard deviation approximately 12 cm.

To find the chance that someone weighs exactly 180 cm

We need to find the Probaility that weighs exactly 180 cm we need to find P[X=180] which is 0 because since X is normal which is a continous distribution then the probability at a point is always zero.

Hence there is approximately 0% chance that someone weighs exactly 180 cm