5.3 Finding Values

Front

What is a z-score?

Back

A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It is expressed in terms of standard deviations from the mean.

Front

How do you find the z-score given a cumulative area?

Back

To find the z-score from a cumulative area, you can use a z-table or statistical software that provides the z-score corresponding to the given cumulative probability.

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean of the data set.

Front

What is the significance of the 5th percentile in a normal distribution?

Back

The 5th percentile indicates the value below which 5% of the data falls. In practical terms, it can represent a cutoff point for a specific requirement, such as weight.

Front

How do you calculate the minimum weight requirement for a cereal box given a mean and standard deviation?

Back

Front

What is the formula for finding the value at a specific percentile in a normal distribution?

Back

Front

What is the 90th percentile in a normal distribution?

Back

The 90th percentile is the value below which 90% of the data falls. It can be found using the z-score corresponding to 0.90.

Front

How do you interpret a z-score of -0.56?

Back

A z-score of -0.56 means the value is 0.56 standard deviations below the mean.

Front

What is the mean and standard deviation of a normally distributed variable?

Back

The mean is the average of the data set, and the standard deviation measures the dispersion or spread of the data around the mean.

Front

What is the cumulative area in relation to z-scores?

Back

The cumulative area represents the probability that a value will fall below a certain z-score in a standard normal distribution.