Normal Distribution and the Empirical Rule (Topic 12)

Front

What is the mean (μ) in a normal distribution?

Back

The mean (μ) is the average value of a dataset, representing the center of the normal distribution curve.

Front

What is the standard deviation (σ) in a normal distribution?

Back

The standard deviation (σ) measures the dispersion or spread of data points around the mean in a normal distribution.

Front

According to the empirical rule, what percentage of data falls within 1 standard deviation from the mean?

Back

Approximately 68% of the data falls within 1 standard deviation from the mean in a normal distribution.

Front

According to the empirical rule, what percentage of data falls within 2 standard deviations from the mean?

Back

Approximately 95% of the data falls within 2 standard deviations from the mean in a normal distribution.

Front

According to the empirical rule, what percentage of data falls within 3 standard deviations from the mean?

Back

Approximately 99.7% of the data falls within 3 standard deviations from the mean in a normal distribution.

Front

What is a z-score?

Back

A z-score indicates how many standard deviations a data point is from the mean. It is calculated as z = (X - μ) / σ.

Front

How do you calculate the z-score for a value of 42, given a mean of 40 and a standard deviation of 1.4?

Back

z = (42 - 40) / 1.4 = 1.43.

Front

What does a z-score of 1.43 indicate?

Back

A z-score of 1.43 indicates that the value is 1.43 standard deviations above the mean.

Front

What is the significance of the highest point of the normal distribution curve?

Back

The highest point of the curve represents the mean (μ) of the distribution.

Front

If a dairy product has a mean shelf life of 12 days and a standard deviation of 3 days, what percent of products last between 12 and 15 days?

Back

Approximately 34% of the products last between 12 and 15 days.