The Normal Distribution

Learning Objectives:

• Understand the normal distribution
• Use Z-scores and standard normal table
• Apply normal approximation

Normal Distribution

$X sim mathcal{N}(mu, sigma^2)$:

f_X(x) = rac{1}{sigmasqrt{2pi}} e^{-(x-mu)^2/(2sigma^2)}

68-95-99.7 Rule:

• 68% within $mu pm sigma$
• 95% within $mu pm 2sigma$
• 99.7% within $mu pm 3sigma$

This lesson covers fundamental concepts in probability theory.

Master these concepts for advanced probability applications.