The Normal Distribution and the Empirical Rule

Poll

I can identify a normal probability distribution, if presented with a graph, histogram or stem and leaf plot.

• Everytime

• Sometimes

• Maybe

• Normal? What?!?

Hotspot

Mark the images that represent a normal probability distribution.

Multiple Choice

Located at the center of a normal distribution is the ________ and it is represented by the symbol, ___.

• mean, μ

• standard deviation, μ

• standard deivation, σ

• mean, σ

Definition

Multiple Choice

All of the below sets have the same mean.
Set 1-Standard Deviation=3.1
Set 2-Standard Deviation=4.9
Set 3-Standard Deviation=1.7
Set 4-Standard Deviation=3.2
Which set of data probably has the points closest to the mean?

• 1

• 2

• 3

• 4

Poll

Where do we place the mean on a normal distribution curve?

• To the left of the middle

• Somewhere close to the middle

• Exactly in the middle, where the curve is highest

• To the right of the middle

Poll

Where would we see standard deviations added to the mean?

• To the left of the middle

• Somewhere close to the middle

• Exactly in the middle, where the curve is highest

• To the right of the middle

Poll

Where would we see standard deviations subtracted from the mean?

• To the left of the middle

• Somewhere close to the middle

• Exactly in the middle, where the curve is highest

• To the right of the middle

Multiple Choice

According to the empirical rule, what is the percentage of data that falls within one standard deviation of the mean?

• 67%

• 65%

• 72%

• 68%

Multiple Choice

Using the empirical rule, what is the percentage of data that falls within two standard deviations of the mean?

• 68%

• 99.7%

• 95%

• 98%

Multiple Choice

What is the percentage of data that falls within three standard deviations of the mean, according to the empirical rule?

• 99.7%

• 98.7%

• 95%

• 100%

Multiple Choice

What percentages of pregnancies last less than 250 days?

• 2.35%

• 13.5%

• 16%

• 34%

Multiple Choice

What percentage of pregnancies are longer than 298 days?

• 0.15%

• 2.35%

• 2.5%

• 13.5%

Multiple Choice

Using the Empirical Rule:

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

• 68%

• 34%

• 16%

• 2.5%

Multiple Choice

A machine is used to put bolts into boxes. It does so such that the actual number of bolts in a box is normally distributed with a mean of 106 and a standard deviation of 2. What is the probability of selecting a box that contains less than 108 bolts?

• 0.84

• .16

• 0.64

• 95

Multiple Choice

Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 

Hint: Sketch the Normal Distribution curve.

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

Multiple Choice

Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

Drag and Drop

2000 freshman at NC State University took a biology test. The scores were distributed normally with a mean of 70 and a standard deviation of 5. What percentage of scores are between 65 and 75?

Placeholder

Drag these tiles and drop them in the correct blank above

68%

34%

50%

99%

Multiple Choice

500 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and standard deviation of 4. Approximately how many juniors scored between 16 and 32?

• 340

• 250

• 475

• 95

Multiple Choice

Which of the following is a disadvantage of the Empirical Rule?

• There is no result for 4 standard deviations.

• It is very conservative.

• There is no result for 1 standard deviation.

• The data has to be approximately normal.

Poll

How did you feel about today's lesson? How confident were you about the material?

• Move over teach....I've got this!!

• Good

• A little shaky

• I really need some help