Chapter 5 Normal Distribution Probabilities 2023

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: about 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Front

How do you calculate the z-score?

Back

Front

What is the significance of the z-table?

Back

The z-table provides the area (probability) to the left of a given z-score in a standard normal distribution, allowing for the calculation of probabilities.

Front

What is the probability of a z-score being less than a certain value?

Back

To find the probability of a z-score being less than a certain value, refer to the z-table to find the corresponding area under the curve.

Front

How do you find the probability of a sample mean?

Back

Front

What is the 75th percentile in a normal distribution?

Back

The 75th percentile is the value below which 75% of the data falls. It can be found using the z-score corresponding to 0.75 in the z-table.

Front

How do you determine the value corresponding to a specific percentile?

Back