Questions: Unit 3 Review: Chapter 5 6 Section 5.1 1. Use the normal curve to estimate the mean and standard deviation.

Unit 3 Review: Chapter 5 6 Section 5.1 1. Use the normal curve to estimate the mean and standard deviation.
Transcript text: a 1342 Unit 3 Review: Chapter 5 \& 6 Section 5.1 1. Use the normal curve to estimate the mean and standard deviation.
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Solution

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Solution Steps

Step 1: Find the mean

The mean of a normal distribution is located at the highest point of the curve. In the given graph, the highest point of the curve corresponds to $x=15$.

Step 2: Find the standard deviation

The standard deviation determines the spread of the normal distribution. One standard deviation away from the mean contains about 68% of the data, two standard deviations away from the mean contains about 95% of the data, and three standard deviations away from the mean contains about 99.7% of the data. In the graph, the dotted lines seem to divide the area under the curve into 6 roughly equal parts (3 to the left of the mean and 3 to the right). Thus, the range from 10 to 20 covers approximately 95% of the data, meaning it represents about two standard deviations away from the mean in either direction. Since the mean is 15, the distance from the mean to 20 is 5 and the distance from the mean to 10 is also 5. Thus, two standard deviations are approximately equal to 5 units. Therefore, one standard deviation is roughly 2.5 units.

Final Answer:

The mean is approximately 15, and the standard deviation is approximately 2.5.

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