5.1 & 5.2 Finding Normal Probabilities

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.

Front

What does the mean represent in a normal distribution?

Back

The mean represents the average value of the data set and is the center of the normal distribution.

Front

What does the standard deviation indicate 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 are closer to the mean.

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 - mean) / standard deviation.

Front

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

Back

To find the probability of a value, convert the value to a z-score and then use the standard normal distribution table to find the corresponding probability.

Front

What is the area under the curve in a normal distribution?

Back

The area under the curve represents the total probability, which is always equal to 1.

Front

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

Back

The empirical rule states that in a normal distribution, approximately 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 calculate the probability of a range of values in a normal distribution?

Back

To calculate the probability of a range, find the z-scores for both values, then find the area under the curve between those z-scores using the standard normal distribution table.

Front

What is the significance of a z-score of 0?

Back

A z-score of 0 indicates that the value is exactly equal to the mean of the distribution.

Front

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

Back

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