Unit 2: Normal Distributions

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

How do you calculate the z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What does a z-score represent?

Back

A z-score indicates how many standard deviations an element is from the mean. A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

Front

What is the empirical rule?

Back

The empirical rule states that for 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

What is the significance of the 95% confidence interval in normal distributions?

Back

A 95% confidence interval means that if you were to take 100 samples, approximately 95 of them would contain the true population mean.

Front

How do you find the area under the normal curve?

Back

The area under the normal curve can be found using z-tables or statistical software, which provide the probability of a value falling within a certain range.

Front

What is a percentile?

Back

A percentile is a measure used to indicate the value below which a given percentage of observations in a group of observations falls.

Front

How do you calculate the percentile rank of a value?

Back

Percentile Rank = (Number of values below X / Total number of values) * 100.

Front

What is the purpose of standard deviation in a normal distribution?

Back

Standard deviation measures the dispersion or spread of a set of values in a distribution. A smaller standard deviation indicates that the values tend to be closer to the mean.