Front

What is a normal distribution?

Back

A normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve, where the mean, median, and mode are all equal.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average value of a dataset and represents the center of the normal distribution.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean in a normal distribution.

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What is the significance of the z-score in statistics?

Back

The z-score indicates how many standard deviations an element is from the mean, helping to understand the relative position of a value in a distribution.

Front

What is the empirical rule (68-95-99.7 rule)?

Back

The empirical rule states that in a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Front

How do you find the percentile of a value in a normal distribution?

Back

To find the percentile, calculate the z-score and then use the standard normal distribution table to find the corresponding percentile.

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What is the area under the normal curve?

Back

The total area under the normal curve is equal to 1, representing the total probability of all outcomes.

Front

What is the purpose of using a normal distribution in statistics?

Back

Normal distribution is used to model real-world phenomena, allowing for the application of statistical methods and inference.

Front

How do you determine the cutoff for the bottom 10% in a normal distribution?

Back

To find the cutoff for the bottom 10%, calculate the z-score that corresponds to the 10th percentile and then convert it back to the original scale using the mean and standard deviation.