1. NORMAL DISTRIBUTIONS
MATH III
LESSON 12 – 2

2. WHAT IS IT? A normal distribution has several key characteristics:
The majority of the data is in the middle
A peak around the mean
“A lot of kids are average.”
Some of the data is lower, some of the data is higher.
Slow decline/incline from the mean.
“Some kids are above/below average.”
Very little of the data is much higher or lower.
Very small slope on the extremes of the graph.
“Only a few make really high or really low grades.

3. WHAT DOES IT LOOK LIKE?
Normal distribution

4. NORMAL OR SKEWED?
Determine whether each set is skewed or normal. Daily Quiz Scores

5. NORMAL OR SKEWED?
Determine whether each set is skewed or normal. Observed speed of passing cars

6. EMPIRICAL RULE (68/95/99.7 rule)
A normal distribution is called normal because things are symmetrically distributed throughout.
68% of the values in the data set are within 1 standard deviation from the mean (34% in each direction)
95% of the values in the data set are within 2 standard deviations from the mean (47.5% in each direction)
99.7% of the values in the data set are within 3 standard deviations from the mean (49.85% in each direction)

7. WHAT DOES IT LOOK LIKE?

8. APPLICATION
A normal distribution of the fuel economy of cars in a company fleet has a mean of 34 and a standard deviation of 5. Draw the distribution. Label the deviations in each direction from the mean. What is the probability a car will Get less than 24 miles per gallon? What is the probability a car will get More than 39 miles per gallon?

9. APPLICATION
The heights of 1800 teenagers are found to be normally distributed with a mean of 66” and a standard deviation of 2”. About how many teens are between 62 and 70” tall? About how many teens are more than 72” tall? About how many teens are less than 58” tall?

10. APPLICATION
Shoe sizes in a class of 32 students are normally distributed with a mean of 8 and a standard deviation of 1.5. Approximately how many of the students have a shoe size less than 6.5? Approximately how many of the students have a shoe size greater than 11?