Is the Bollinger Bands assumption wrong?

Bollinger Bands are the result of the assumption that closing prices will follow a normal distribution.

However, when I actually calculated the probability, the closing price does not follow a normal distribution.

According to the normal distribution, the probability that Z > 2 should be 2.2%, but on the chart, the probability is 6~9%.



Can we get a useful value for Bollinger Bands that we can use in our strategy?

We can measure volatility, but can we judge volatility based on a fixed value?



To the right of each Bollinger band value, the probability that the price is above the band is displayed.

The script is simply annotated with how each probability is calculated.