4/8 Normal Distribution Curves

What shape is a normal distribution curve?

• Half curve

• Rhombus curve

• Bell curve

• Square curve

Answer explanation

A normal distribution curve is a symmetrical bell-shaped curve defined by the mean $\left(\mu\right)$ and the standard deviation $\left(\sigma\right)$ of the data set.

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What does the mean tell you about a data set

• It tells you the number that occurs the most

• It is the difference between the highest and lowest number

• It tells you the average of the data set

• It tells you how mad someone is at another persom

Answer explanation

When referring to the average of a data set, we use the term 'mean'.

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Given a mean of 75 and a standard deviation of 7, what percentage of scores are above 82?

• 34%

• 81.5%

• 16%

• 2.5%

Answer explanation

If the mean is 75 then $1\sigma$ is 82. The question is asking for the percentage for all scores above an 82, including outliers. Determine the percentages for the area under the curve for $1\sigma$ and above.

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Given a mean of 75 and a standard deviation of 7, what percentage of scores are between 54 and 96?

• 13.59%

• 99.73%

• 95.44%

• 2.14%

Answer explanation

If the mean is 75 then $-3\sigma$ is 54 and $3\sigma$ is 96. Determine the percentages for the area under the curve from $-3\sigma\ to\ 3\sigma$ .

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Given a mean of 75 and a standard deviation of 7, what percentage of scores are greater than 68?

• 34%

• 84%

• 95%

• 68%

Answer explanation

If the mean is 75 then $-1\sigma$ is 68. Determine the percentages for the area under the curve above $-1\sigma$ .

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Where can we locate the mean in the normal curve?

• On the left side of the curve.

• On the right side of the curve.

• At the center of the curve.

• With the outliers.

Answer explanation

The mean $\left(\mu\right)$ is the at the center of a normal distribution curve.

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What is the total area under the normal curve in a standard normal distribution?

• 1

• 2

• 3

• 4

Answer explanation

The area under the curve represents probability, with the total area equal to one.

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This data is normally distributed. What percent of the data is in the shaded region?

• 68%

• 95%

• 99.7%

• 50%

Answer explanation

The mean $\left(\sigma\right)$ is the center of the curve. The lower half of the curve is shaded. If the area under the curve equals 1, then half of the area under the curve equals .50.

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This data is normally distributed.  What percent of the data is in the shaded region?

• 68%
• 95%
• 99.7%
• 50%

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This data is normally distributed. What percent of the data is in the shaded region?

• 68.2%

• 95.4%

• 99.7%

• 50%

Answer explanation

In a normal distribution with a mean $\left(\mu\right)$ and a standard deviation $\left(\sigma\right)$ , approximately 68.2% of the data falls within $1\sigma$ of the mean, approximately 95.4% of the data falls within $2\sigma$ of the mean and approximately 99.8% of the data falls within $3\sigma$ of the mean.

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