Understanding Z-Scores and Probability

This video tutorial explains how to use Z-score tables to find probabilities in a normal distribution. It covers calculating probabilities for Z-scores below, above, and between given values using cumulative and zero to Z tables. Two examples demonstrate these calculations, including handling negative Z-scores using symmetry.

What is the purpose of using tables in relation to Z-scores?

• To identify outliers in the data

• To find the mean of a data set

• To calculate the standard deviation

• To determine probabilities related to Z-scores

Which table provides the area to the left of a given Z-score?

• Standard deviation table

• Cumulative table

• Zero to Z table

• Mean table

How do you find the probability of a Z-score being greater than a given value?

• Multiply the cumulative probability by 2

• Divide the cumulative probability by 2

• Add the cumulative probability to 1

• Subtract the cumulative probability from 1

In the example, what is the probability of a Z-score being less than 1.4?

• 0.9192

• 0.6736

• 0.0808

• 0.5000

What is the probability of a Z-score being greater than 1.4?

• 0.5000

• 0.9192

• 0.6736

• 0.0808

How do you find the probability of a Z-score being between two values?

• Use the cumulative table for both values

• Use the zero to Z table for both values and add the areas

• Multiply the probabilities of both Z-scores

• Subtract the smaller Z-score from the larger one

What is the probability of a Z-score being between -0.5 and 2.1?

• 0.9192

• 0.0808

• 0.5000

• 0.6736

Why do we use symmetry for negative Z-scores?

• To increase accuracy

• To avoid errors

• To simplify calculations

• Because negative Z-scores are not in the table

What is the area between Z equals zero and Z equals negative 0.5?

• 0.9192

• 0.6736

• 0.4821

• 0.1915

What is the area between Z equals zero and Z equals 2.1?

• 0.6736

• 0.9192

• 0.1915

• 0.4821