[Verse 1] Picture data scattered like confetti in the wind Some points cluster near the middle, that's where patterns begin A mountain made of frequencies, symmetric and complete The normal distribution makes our financial picture sweet [Chorus] Bell curve beauty, sixty-eight percent within one standard Ninety-five in two, ninety-nine point seven in three standard Z-score transforms any normal to the same playing field Subtract the mean, divide by sigma, watch the magic yield [Verse 2] Stock returns and portfolio gains follow nature's law Random walks and market moves, the bell curve holds them all Mean regression pulls the outliers back toward the center Risk and volatility calculations, this is where we enter [Chorus] Bell curve beauty, sixty-eight percent within one standard Ninety-five in two, ninety-nine point seven in three standard Z-score transforms any normal to the same playing field Subtract the mean, divide by sigma, watch the magic yield [Bridge] Standardize your thinking, make comparisons precise Any normal curve becomes the same statistical device Mu for mean and sigma squared for variance we need The central limit theorem plants this powerful seed [Verse 3] Value at Risk calculations, confidence intervals too Portfolio optimization depends on what these curves can do Asset pricing models lean on normal assumptions strong Though markets sometimes misbehave, this tool still carries on [Chorus] Bell curve beauty, sixty-eight percent within one standard Ninety-five in two, ninety-nine point seven in three standard Z-score transforms any normal to the same playing field Subtract the mean, divide by sigma, watch the magic yield [Outro] From minus three to plus three, probabilities unfold The normal distribution, worth its weight in gold
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