Introduction to Normal Distribution

Normal Distribution Curve

​Review of what we have talked about so far concerning normal distribution

Remember a normal distribution is a bell curve shape.

​It is symmetric with respect to the mean or middle.

Multiple Choice

What type of distribution is pictured?

• Right skewed

• Left skewed

• Random

• Normal

Multiple Choice

Even though it is not exactly perfect, this is still considered a normal distribution. It just has to be mostly normal looking.

• TRUE

• FALSE

Mean

The mean is always at the center of the normal distribution curve. We use the Greek letter "μ" to denote this number. It is called mu, and you pronounce it "m-you"

Fill in the Blanks

What is the mean on the graph given?

Fill in the Blanks

What is the mean on the graph given?

Standard Deviation

We add and subtract standard deviations from the mean. We use the Greek letter "σ" to denote this number. It is called sigma, and you pronounce it just like it looks. In the graph to the right, two standard deviations below the average would be the number 25, and we would call this μ-2σ.

Fill in the Blanks

What is the standard deviation on the graph given? In other words, how is 18 turning into 20 and 20 turning into 22? What is that amount?

Fill in the Blanks

What is the standard deviation on the graph given?

Multiple Choice

Algebra reminder: $$\mu+\sigma=\mu+1\sigma$$ . We need to know that one standard deviation above the average is $$\mu+1\sigma$$ , but we usually don't see the 1. Same things goes for $$\mu-\sigma=\mu-1\sigma$$ .

• Got it, Ms. Davis!

• I hate algebra, so I refuse to believe this nonsense.

Fill in the Blanks

What is $\mu+\sigma$ ? In other words, what is the number that is one standard deviation to the right of the mean of 35?

Fill in the Blanks

What is $\mu+2\sigma$ ?

Fill in the Blanks

What is $\mu-\sigma$ ?

Fill in the Blanks

What would $\mu-3\sigma$ be, even though it is not labeled on the graph?

Fill in the Blanks

What would $\mu+3\sigma$ be, even though it is not labeled on the graph?

Empirical Rule

68% of the data lies within ± one standard deviation

95% of the data lies within ± two standard deviations

99.7% of the data lies within ± three standard deviations

Multiple Choice

From 30 to 40 covers ___% of the data.

• 68
• 95

• 99.7

• 100

Multiple Choice

From 25 to 45 covers ___% of the data.

• 68
• 95

• 99.7

• 100

Multiple Choice

From 20 to 50 covers ___% of the data.

• 68
• 95

• 99.7

• 100