Normal Distribution - Discrete or Continuous?

[Procrastinate]

Suppose that the height of adult females in a population is a normal random variable with a
mean of 165 cm and a standard deviation of 12 cm. If heights are measured to the nearest
centimetre, what percentage of the adult female population will have a measured height between 150 and 160 cm?


I know that height is generally considered as continuous data but I thought that this case was an discrete because it said "measured to the nearest centimetre."

However, I plugged in the numbers into my calculation (Lower: 149.5 and Upper:160.5) and got 25.56% as my answer. However, the textbook says that the answer is .2328 (23.28%) which is what you would get if you plugged in Lower: 150 and Upper 160 i.e. continuous values.

I am not sure whether that is right but I easily could be wrong. Could someone tell me their opinion?

 

[micromass]

Well, in theory you are correct. If the question is phrased like that, then it is a discrete.

But... textbooks are stupid I think they didnt think of this when they wrote this question.

So next time, if you read in a textbook that we have a normal random variable, then it is continuous (even if the rest of the information doesn't agree).