Normal Distribution Probability Problems

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What are the key characteristics of a normal distribution?

Back

1. Symmetrical shape. 2. Mean, median, and mode are all equal. 3. The total area under the curve is 1. 4. Approximately 68% of data falls within one standard deviation of the mean.

Front

What is the mean in a normal distribution?

Back

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

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean.

Front

How do you calculate the z-score?

Back

Front

What does a positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean.

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean.

Front

What is the 75th percentile in a normal distribution?

Back

The 75th percentile is the value below which 75% of the data falls.

Front

How do you find the probability of a value being less than a certain number in a normal distribution?

Back

You can find this probability using the z-score and a standard normal distribution table or calculator.

Front

What is the area under the normal distribution curve?

Back

The area under the normal distribution curve represents the total probability and is equal to 1.