Questions: Which of the following are characteristics of a normal distribution? The normal distribution curve is symmetric about the standard deviation of the mean is approximately 1.68 The total area under the curve is 1.00 The mean, median, and mode are located at the center of the distribution curve is 100 The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.95

Which of the following are characteristics of a normal distribution? The normal distribution curve is symmetric about the standard deviation of the mean is approximately 1.68 The total area under the curve is 1.00 The mean, median, and mode are located at the center of the distribution curve is 100 The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.95
Transcript text: Which of the following are characteristics of a normal distribution? The normal distribution curve is symmetric about the standard deviation of the mean is approximately 1.68 The total area under the curve is 1.00 The mean, median, and mode are located at the center of the distribution curve is 100 The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.95
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Solution

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Solution Steps

Step 1: Nature of Distribution

The normal distribution is a ^continuous^ probability distribution, covering all possible values within a range.

Step 2: Symmetry and Shape

The distribution is ^symmetric^ about the mean and is ^bell-shaped^, indicating a normal distribution.

Step 3: Mean, Median, Mode Location

In a normal distribution, the ^mean^, ^median^, and ^mode^ are all located at the ^same point^, at the center of the distribution.

Step 4: Area Under the Curve

Approximately ^68%^ of the data falls within 1 standard deviation of the mean, ^95%^ within 2 standard deviations, and ^99.7%^ within 3 standard deviations.

Step 5: Total Area Under the Curve

The total area under a normal distribution curve is ^1^, representing the total probability of all outcomes.

Step 6: Curve Crossing the X-axis

The normal distribution curve ^approaches but never touches the x-axis^, as it is asymptotic.

Final Answer:

Given the parameters, the distribution is confirmed to be a ^normal distribution^ with all characteristics aligning with the theoretical properties of normal distributions.

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