Understanding Normal Distribution

What is a Z-score and how is it calculated?

• A Z-score indicates the average of all values in a dataset.

• A Z-score is a measure of the total number of data points in a dataset.

• A Z-score is calculated by adding all values in a dataset together.

• A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values.

How do you interpret a Z-score of 1.5?

• The data point is exactly at the mean.

• The data point is 1.5 times the mean value.

• The data point is 1.5 standard deviations above the mean.

• The data point is 1.5 standard deviations below the mean.

What is the mean and standard deviation of a standard normal distribution?

• Mean: 0, Standard Deviation: 2

• Mean: 0, Standard Deviation: 1

• Mean: -1, Standard Deviation: 1

• Mean: 1, Standard Deviation: 0

How do you find the probability of a Z-score using a Z-table?

• Locate the Z-score in the Z-table and read the corresponding probability.

• Use the Z-score to calculate the standard deviation directly.

• Add the Z-score to the mean of the dataset.

• Multiply the Z-score by 100 to get the probability.

If a Z-score is -2, what area under the curve does it represent?

• 0.5000

• 0.8413

• 0.1587

• 0.0228

What is the total area under a normal distribution curve?

• 0.5

• 1.5

• 2

• 1

How do you find the area to the left of a given Z-score?

• Multiply the Z-score by 100 to convert it to a percentage.

• Subtract the Z-score from 1 to get the area.

• Use a calculator to find the area under the curve.

• Use a Z-table to find the cumulative probability for the given Z-score.

What is the relationship between Z-scores and percentiles?

• Z-scores and percentiles are related; higher Z-scores correspond to higher percentiles.

• Z-scores are only applicable to normal distributions, while percentiles apply to all distributions.

• Z-scores and percentiles are unrelated; they measure different concepts.

• Higher percentiles always correspond to lower Z-scores.

How can you use a Z-table to find the probability of a range of Z-scores?

• Use the Z-table to find the mean of the Z-scores.

• Add the cumulative probabilities of the two Z-scores.

• Multiply the cumulative probabilities of the two Z-scores.

• Subtract the cumulative probabilities of the two Z-scores.

What does it mean if a Z-score is greater than 3?

• The data point is less than average.

• The data point is an outlier.

• The data point is within the normal range.

• The data point is the mean.