## Normal Random Variables (3 of 6)

### Learning Objectives

• Use a normal probability distribution to estimate probabilities and identify unusual events.

## The Empirical Rule in a Context

Suppose that foot length of a randomly chosen adult male is a normal random variable with mean $\mathrm{μ}=11$ and standard deviation $\mathrm{σ}=1.5$ . Then the empirical rule lets us sketch the probability distribution of X as follows:

• (a) What is the probability that a randomly chosen adult male will have a foot length between 8 and 14 inches?
• (b) An adult male is almost guaranteed (0.997 probability) to have a foot length between what two values?
• Answer: 6.5 and 15.5 inches
• (c) The probability is only 2.5% that an adult male will have a foot length greater than how many inches?