Exploring the Empirical Rule in Normal Distribution

Miss Ha introduces lesson 87 on normal distribution and the empirical rule. The lesson begins with a comparison between normal and uniform distributions, highlighting the bell-shaped curve of normal distribution. The empirical rule is explained, stating that nearly all data in a normal distribution falls within three standard deviations of the mean. The lesson covers the area under a normal curve and provides a practical example using bolts in boxes to illustrate the empirical rule.

What shape does the graph of normally distributed data typically have?

• Bell-shaped

• Skewed

• Uniform

• Bimodal

Which of the following is an example of data that is uniformly distributed?

• Blood pressure of randomly selected males

• Weights of newborn babies

• Heights of students in a class

• Number that comes up on the roll of a fair die

Tags

CCSS.7.SP.C.7A

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

• 68%

• 50%

• 95%

• 99.7%

Tags

CCSS.HSS.ID.A.4

What is another name for the empirical rule?

• Chebyshev's Inequality

• Three Sigma Rule

• Central Limit Theorem

• Law of Large Numbers

Tags

CCSS.6.SP.B.5C

What is the total area under a normal distribution curve?

• 1

• 2

• 0.5

• 3

Approximately what percentage of the area lies within two standard deviations of the mean in a normal distribution?

• 99.7%

• 50%

• 95%

• 68%

Tags

CCSS.HSS.ID.A.4

In the example of bolts in boxes, what is the mean number of bolts?

• 104

• 106

• 108

• 110

Tags

CCSS.6.SP.B.5C

If the standard deviation is 2, what is the number of bolts at two standard deviations above the mean?

• 108

• 110

• 112

• 114

What percentage of data lies between 104 and 108 bolts in the given example?

• 95%

• 68%

• 50%

• 34%

Tags

CCSS.HSS.ID.A.4

In the context of the example, how many standard deviations below the mean is 104 bolts?

• Three

• Two

• One

• Zero