Understanding the Standard Normal Distribution

This video tutorial introduces the concept of the standard normal distribution and z-scores. It explains how to calculate a z-score, which represents the number of standard deviations a data value is from the mean. The tutorial covers the properties of the standard normal distribution, which has a mean of zero and a standard deviation of one, and applies the empirical rule to describe data distribution. Two examples are provided: one calculates a z-score from a test score, and the other finds a test score from a given z-score.

What is a z-score?

• A measure of central tendency

• The number of standard deviations a data value is from the mean

• A measure of data spread

• A type of probability distribution

How is a z-score calculated?

• By adding the mean to the data value

• By dividing the data value by the mean

• By multiplying the data value by the standard deviation

• By subtracting the mean from the data value and dividing by the standard deviation

What is the mean of the standard normal distribution?

• 1

• 100

• 0

• Depends on the data

What is the standard deviation of the standard normal distribution?

• 1

• 0

• Depends on the data

• 100

According to the empirical rule, what percentage of data falls within one z-score of the mean?

• 95%

• 68%

• 99.7%

• 50%

What does the empirical rule state about data within three z-scores of the mean?

• 99.7% of data falls within this range

• All data falls within this range

• 95% of data falls within this range

• 68% of data falls within this range

What is the z-score for a test score of 500 if the mean is 550 and the standard deviation is 80?

• 1.25

• 0.625

• -0.625

• -1.25

What does a negative z-score indicate?

• The data value is below the mean

• The data value is above the mean

• The data value is equal to the mean

• The data value is an outlier

If a test score is 1.2 standard deviations above the mean, what is the z-score?

• 0

• 2.4

• 1.2

• -1.2

What test score corresponds to a z-score of 1.2 if the mean is 550 and the standard deviation is 80?

• 630

• 500

• 550

• 646