Normal Distribution - Discrete or Continuous?

In summary, we are discussing the height of adult females in a population, which is a normal random variable with a mean of 165 cm and a standard deviation of 12 cm. The question asks what percentage of the population will have a measured height between 150 and 160 cm, assuming measurements are to the nearest centimetre. While some argue that this makes it a discrete variable, the generally accepted answer is 23.28%, using continuous values of 150 and 160 cm. However, there may be room for interpretation and different opinions on this matter.
  • #1
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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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  • #2
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).
 

Related to Normal Distribution - Discrete or Continuous?

1. What is a normal distribution?

A normal distribution is a type of probability distribution that is often used to represent the distribution of data in a population. It is also known as a Gaussian distribution, and is characterized by a bell-shaped curve with the highest frequency at the mean and symmetrical tails on either side.

2. Is normal distribution discrete or continuous?

Normal distribution can be either discrete or continuous, depending on the type of data being represented. If the data is measured on a continuous scale, such as height or weight, then the normal distribution is continuous. If the data is measured on a discrete scale, such as the number of students in a class, then the normal distribution is discrete.

3. What are the properties of a normal distribution?

A normal distribution has several important properties, including symmetry, a single peak at the mean, and the majority of the data falling within a few standard deviations of the mean. It also follows the 68-95-99.7 rule, where approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

4. How is the normal distribution used in statistics?

The normal distribution is used in statistics to make predictions about the likelihood of certain events occurring, based on the data being normally distributed. It is also used to calculate probabilities and to estimate the confidence intervals for a given set of data. In addition, many statistical tests and models assume a normal distribution of data.

5. Can a data set have a normal distribution if it has outliers?

In general, a data set with outliers cannot be considered a normal distribution. Outliers, which are data points that are significantly different from the rest of the data, can greatly affect the shape and properties of a normal distribution. However, if the number of outliers is small and the data still meets the criteria for a normal distribution, it may still be considered as such.

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