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Because you are plotting values randomly sampled from a normal distribution against the normal distribution itself - i.e. the values on the x and y axis are virtually the same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the density of observations would not out at either end, as it would be even (the number of observations in 5% of the data would be equal regardless of whether it was the 5% closest or furthest from the mean). For example, try amending your code to increase the number of random samples e.g. change x <- rnorm(1000) to x <- rnorm(10000), and the axes will adjust to include the 4th standard deviation.

Because you are plotting values randomly sampled from a normal distribution against the normal distribution itself - i.e. the values on the x and y axis are virtually the same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the frequency of observations would not peter out at either end: instead it would be constant. For example, try amending your code to increase the number of random samples e.g. change x <- rnorm(1000) to x <- rnorm(10000), and the axes will adjust to include the 4th standard deviation.

Because you are plotting values randomly sampled from a normal distribution against the normal distribution itself - i.e. the values on the x and y axis are virtually the same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the density of observations would not out at either end, as it would be even (the number of observations in 5% of the data would be equal regardless of whether it was the 5% closest or furthest from the mean). For example, try amending your code to increase the number of random samples i.e. change x <- rnorm(1000) to x <- rnorm(10000), and the axes will adjust to include the 4th standard deviation.

Because you are plotting values randomly sampled from a normal distribution against the normal distribution itself - i.e. the values on the x and y axis are virtually the same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the density of observations would not out at either end, as it would be even (the number of observations in 5% of the data would be equal regardless of whether it was the 5% closest or furthest from the mean). For example, try amending your code to increase the number of random samples e.g. change x <- rnorm(1000) to x <- rnorm(10000), and the axes will adjust to include the 4th standard deviation.

Because you are plotting values randomly sampled from a normal distribution against the normal distribution istelf - i.e. the values on the x and y axis are the virtually same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the density of obersvations would not out at either end, as it would be even (the number of observations in 5% of the data would be equal regardles off whether it was the 5% closest or furthest from the mean). For example, try amending your code to increase the number of random samples i.e change x<-rnorm(1000) to x<-rnorm(10000), and the axes will adjust to include the 4th standard deviation.

Because you are plotting values randomly sampled from a normal distribution against the normal distribution itself - i.e. the values on the x and y axis are virtually the same by definition - and are the same in the limit.

In answer to your second question note that the scale on the figure shown is number of std deviations from the mean, which has no upper or lower bound. If the scale related to proportion of observations, then the scale would be defined to be between 0 and 1 (or 0% and 100%), and the density of observations would not out at either end, as it would be even (the number of observations in 5% of the data would be equal regardless of whether it was the 5% closest or furthest from the mean). For example, try amending your code to increase the number of random samples i.e. change x <- rnorm(1000) to x <- rnorm(10000), and the axes will adjust to include the 4th standard deviation.