Exploring the Normal Distribution in Algebra II

This video tutorial by Kirk Weiler covers the concept of normal distribution, often visualized as a bell curve. It explains how data is distributed around the mean and the significance of standard deviations. Through exercises, the tutorial demonstrates how to calculate the percentage of data within one, two, and three standard deviations from the mean. It also applies these concepts to real-world examples, such as SAT scores, to illustrate how to determine percentiles and interpret data using z-scores.

What is the shape of a normal distribution?

• A zigzag pattern

• A straight line

• A bell curve

• A U-shape

In a perfect normal distribution, what percentage of data lies between the mean and half a standard deviation above the mean?

• 30.0%

• 15.0%

• 19.1%

• 25.0%

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CCSS.HSS.ID.A.4

What percentage of data falls within one standard deviation of the mean in a normal distribution?

• 95.4%

• 68.2%

• 50.0%

• 75.0%

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CCSS.HSS.ID.A.4

If 95.4% of data falls within two standard deviations of the mean, what percentage falls within three standard deviations?

• 99.8%

• 50.0%

• 95.4%

• 68.2%

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CCSS.HSS.ID.A.4

What is the z-score of a data point that is one and a half standard deviations above the mean?

• 2.0

• 1.5

• 1.0

• 0.5

If a student scores 740 on a normally distributed exam with a mean of 540 and a standard deviation of 80, how many standard deviations above the mean is this score?

• 3.0

• 3.5

• 2.0

• 2.5

What percentage of students scored better than a student who is 2.5 standard deviations above the mean?

• 0.5%

• 0.1%

• 1.0%

• 0.6%

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CCSS.HSS.ID.A.4

If the mean weight of a sample of crabs is 12.6 pounds with a standard deviation of 1.5 pounds, what is the weight range for one standard deviation above and below the mean?

• 11.1 to 14.1 pounds

• 10.1 to 15.1 pounds

• 10.1 to 14.1 pounds

• 11.1 to 13.1 pounds

How many crabs out of 250 would be expected to weigh less than 11.1 pounds if the weights are normally distributed with a mean of 12.6 pounds and a standard deviation of 1.5 pounds?

• 35

• 30

• 17

• 25

If fishermen must throw back any crab caught below 10.4 pounds, what percentage of crabs will need to be thrown back if the weights are normally distributed with a mean of 12.6 pounds and a standard deviation of 1.5 pounds?

• 20.0%

• 15.9%

• 9.2%

• 6.7%