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.
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.