Z-Score Probability Calculations

This video tutorial explains how to determine the probability of a randomly selected data value from a normal distribution having a z-score within a given interval. It covers three examples: finding the probability for z-scores less than -1.5, greater than -1.5, and between -0.4 and 1.8. The tutorial uses a z-score table to calculate these probabilities, demonstrating the process of locating z-scores on the table and interpreting the corresponding probabilities.

What is the purpose of using a z-score table in probability calculations?

• To find the mean of a distribution

• To determine the probability left of a z-score

• To calculate the standard deviation

• To identify the mode of a dataset

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CCSS.HSS.ID.A.4

How do you find the probability of a z-score being less than a specific value?

• Subtract the z-score from 50%

• Locate the z-score in the table and use the corresponding percentage

• Multiply the z-score by 2

• Add the z-score to 100%

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CCSS.HSS.ID.A.4

What is the probability of a z-score being less than -1.5?

• 93.32%

• 50%

• 6.68%

• 100%

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CCSS.HSS.ID.A.4

How do you calculate the probability of a z-score being greater than a given value?

• Subtract the percentage from the table from 100%

• Multiply the percentage by 2

• Divide the percentage by 2

• Add the percentage from the table to 100%

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CCSS.HSS.ID.A.4

What is the probability of a z-score being greater than -1.5?

• 100%

• 50%

• 93.32%

• 6.68%

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CCSS.HSS.ID.A.4

How do you find the probability of a z-score falling between two values?

• Add the probabilities of both z-scores

• Subtract the smaller percentage from the larger percentage

• Multiply the probabilities of both z-scores

• Divide the larger percentage by the smaller percentage

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CCSS.HSS.ID.A.4

What is the probability of a z-score being between -0.4 and 1.8?

• 34.46%

• 96.41%

• 61.95%

• 100%

Why do we subtract percentages when finding the probability between two z-scores?

• To isolate the probability within the interval

• To calculate the mean of the probabilities

• To find the probability to the left of the z-score

• To find the probability to the right of the z-score

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CCSS.HSS.ID.A.4

What does the percentage from the z-score table represent?

• The standard deviation

• Probability to the left of the z-score

• The mean of the distribution

• Probability to the right of the z-score

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CCSS.HSS.ID.A.4

What is the first step in finding the probability of a z-score between two values?

• Multiply the two z-scores

• Locate both z-scores in the table

• Add the two z-scores

• Subtract the z-scores from 100%

Tags

CCSS.HSS.ID.A.4