Normal Distribution and Inverse Normal Distribution

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. It is defined by its mean (μ) and standard deviation (σ).

Front

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

Back

The empirical rule states that for a normal distribution: about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What is the mean in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center of the normal distribution curve.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of 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 does a z-score represent?

Back

A z-score represents the number of standard deviations a data point is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is the inverse normal distribution?

Back

The inverse normal distribution is used to find the value of a variable given a specific percentile or probability in a normal distribution.

Front

How do you find the area under the normal curve?

Back

The area under the normal curve can be found using z-scores and standard normal distribution tables or software that calculates probabilities.

Front

What is the significance of the 50th percentile in a normal distribution?

Back

The 50th percentile corresponds to the mean in a normal distribution, meaning that half of the data points fall below this value.

Front

How do you determine the percentage of data within a certain range in a normal distribution?

Back

To determine the percentage of data within a certain range, calculate the z-scores for the endpoints of the range and use the standard normal distribution table to find the corresponding probabilities.