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

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.

Multiple Choice

What percent of people within 3 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

What percent of people within 2 standard deviations of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

What percent of people within 1 standard deviation of the mean?

• 99.7

• 34

• 68

• 95

Multiple Choice

What percentage of the data is between 1 and 2 standard deviations

• 34%

• 50%

• 2.35%

• 13.5%

Multiple Choice

What percentage of the data is between -1 and -2 standard deviations

• 34%

• 50%

• 2.35%

• 13.5%

Multiple Choice

What percent of people are 3 standard deviations above the mean?

• .15

• 34

• 68

• 2.35

Multiple Choice

What shape is a normal distribution curve?

• Half curve
• Round curve
• Bell curve
• Square curve

Multiple Choice

This data is:

• Normally distributed

• Skewed left

• Skewed right