Normal Distribution - Discrete or Continuous?

AI Thread Summary
The discussion centers on the classification of height as a normal random variable, debating whether it should be treated as discrete or continuous data. While height is typically continuous, the mention of measurement to the nearest centimeter raises questions about its classification. Calculations using different ranges yield differing percentages, with one participant obtaining 25.56% using a discrete approach and the textbook providing 23.28% based on continuous values. The consensus suggests that textbooks often assume normal variables are continuous, regardless of specific measurement details. Ultimately, the conversation highlights the complexities in interpreting statistical data classifications.
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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?
 
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Well, in theory you are correct. If the question is phrased like that, then it is a discrete.

But... textbooks are stupid :smile: 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).
 

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