MATH 1040 - Introduction to Statistics

Lesson 16: Real-life scenarios of Normal Distributions

In Lesson 15, we learned about the structure of Normal Distributions. In Lesson 16, we are going to focus on using normal distributions in more real-life scenarios.

Quick example

As CEO of my business, I do an quarterly review with my financing department. I find that my annual budget towards the utilities in the building has a mean of $276,000 with a standard deviation of $17,500. What is the probability that I will spend less than $250,000 on utilities for this upcoming year?

\[z = \frac{\$250,000 - \$276,000}{\$17,500} = \frac{-26000}{17500} = -1.486\]

Using a Z-Table,

\[P(z < -1.486) = 0.069\]

So, there is only a 6.9% chance of spending less than $250,000 on utilities next year.

Topics in this lecture