Suppose X is a continuous random variable such that A figure skating routine is designed to last six minutes. The amount of time (in minutes) less than or greater than six minutes is a random...

Suppose X is a continuous random variable such that

A figure skating routine is designed to last six minutes. The amount of time (in minutes) less than or greater than six minutes is a random variable, X, with a probability density function given by

If the value of X is negative, then the routine was shorter than six minutes; if the value of X is positive, the routine went too long

Let the random variable Z have a standard normal distribution. Find each of the following probabilities and carefully sketch a graph corresponding to each expression.