Download Guided Notes on the Normal Distribution and Empirical Rule

Guided Notes on the Normal Distribution and Empirical Rule Normal Distribution The Normal Distribution is a type of ____________________________. The graph of a Normal Distribution is called a ____________________________ or more commonly referred to as ____________________________. Properties of the Normal Distribution: •
The mean, median, and mode are ____________________________ •
____________________________ about the mean •
Area under the curve equals ____________________________ •
Curve never ____________________________ the x-­‐axis Limits to the mean and standard deviation •
The mean, or μ, ranges between __________________ and __________________. •
The standard deviation, or σ, must be ____________________________. Regardless of the height or width of the curve the areas under each of these curves is always equal to 1.
If the graph is more spread out, like the one in the middle, it has a ____________________________. Empirical Rule Since the ___________________lies in the middle of the curve approximately ___________________ of the data falls below the mean. Consider moving one standard deviation in each direction from the mean (blue area). ________________ of the data falls within this region. For two standard deviations in each direction from the mean (red and blue areas) ________________ of the data lies. Within three standard deviations of the mean (green, red, and blue areas) ________________ of the data lies. ________________ of the data lies outside of three standard deviations of the mean. An auto repair shop states that an average oil change will take 20 minutes. It has been found that the data is normally distributed with a standard deviation of 1.5 minutes. What is the probability that an oil change will be completed in less than 21.5 minutes? Completed in over 23 minutes? Guide to answering these types of questions: •
Determine if the Normal Distribution is valid to use •
Draw a picture •
Label the key points (mean and standard deviations) •
Shade the area you are being asked about •
Answer the question