Normal Distribution Question Bank

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 does the standard deviation represent in a normal distribution?

Back

The standard deviation measures the dispersion or spread of the data points around the mean. A smaller standard deviation indicates that the data points tend to be closer to the mean.

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 one standard deviation, 95% within two standard deviations, and 99.7% within three standard deviations of the mean.

Front

How do you find the area under the normal distribution curve between two z-scores?

Back

To find the area between two z-scores, you can look up the z-scores in the standard normal distribution table and subtract the smaller area from the larger area.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. It is calculated as (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What percentage of data falls below the mean in a normal distribution?

Back

50% of the data falls below the mean in a normal distribution.

Front

How do you calculate the percentage of data above a certain value in a normal distribution?

Back

To calculate the percentage of data above a certain value, find the z-score for that value, look up the corresponding area in the z-table, and subtract it from 1.

Front

What is the significance of the mean in a normal distribution curve?

Back

The mean is the center of the normal distribution curve, where the highest point of the curve occurs, representing the average of the data.

Front

If the mean life of a tire is 30,000 km and the standard deviation is 2000 km, what is the range for 68% of tires?

Back

68% of tires will have a life between 28,000 km and 32,000 km.