Normal Distributions Test

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 does the mean represent in a normal distribution?

Back

The mean (μ) represents the average value of the data set and is the center of the normal distribution curve.

Front

What does the standard deviation indicate in a normal distribution?

Back

The standard deviation (σ) measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points are closer to the mean.

Front

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

Back

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

Front

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

Back

To find the probability of a value in a normal distribution, you can use the z-score formula: z = (X - μ) / σ, and then refer to the standard normal distribution table.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations a data point is from the mean. It is calculated using the formula: z = (X - μ) / σ.

Front

What is the area under the normal curve?

Back

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

Front

How do you find the area between two z-scores?

Back

To find the area between two z-scores, calculate the area to the left of each z-score using the standard normal distribution table and subtract the smaller area from the larger area.

Front

What is the significance of the area to the right of a z-score?

Back

The area to the right of a z-score represents the probability of obtaining a value greater than that z-score in a normal distribution.

Front

What does it mean if a z-score is negative?

Back

A negative z-score indicates that the data point is below the mean of the distribution.