Normal Distribution - Discrete or Continuous?

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SUMMARY

The discussion centers on the classification of height as a normal random variable, specifically questioning whether it is discrete or continuous. The example provided involves adult female heights with a mean of 165 cm and a standard deviation of 12 cm, leading to a calculation of the percentage of the population with heights between 150 and 160 cm. The participant calculated 25.56% using discrete values but noted a discrepancy with the textbook's continuous calculation of 23.28%. The consensus is that normal variables are treated as continuous, regardless of measurement precision.

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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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