The normal distribution and continuous random variables

Learning objectives

Describe the properties of the normal distribution and its bell-shaped curve, and use its symmetry to represent probabilities as areas on a sketch

Calculate normal probabilities and expected frequencies using technology, and use the inverse normal to find the values of x that correspond to given probabilities

Standardise a normal variable using z = (x − μ)/σ, and use z-values to find an unknown mean and/or standard deviation from given probabilities

(HL) Work with a continuous random variable defined by a probability density function: verify that a function is a valid pdf, find unknown constants and calculate probabilities by integration

(HL) Find the mode and median of a continuous random variable, and calculate the mean, variance and standard deviation of discrete and continuous random variables

(HL) Determine the effect of a linear transformation on a random variable using E(aX + b) = aE(X) + b and Var(aX + b) = a²Var(X)