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.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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.

Tags

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.ID.A.4

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.

Tags

CCSS.HSS.ID.A.4

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.