Exploring Areas and Z Scores in Standard Normal Distribution

This video tutorial explains the concept of normal distribution and its properties, focusing on the use of z-scores to calculate probabilities. It provides a detailed example using commuting time data to demonstrate how to find probabilities for values less than, between, and greater than certain points on a standard normal distribution curve. The tutorial also covers how to use z-score tables to find these probabilities and emphasizes the importance of understanding the area under the curve as a representation of probability.

What is a key characteristic of a normal distribution?

• It is symmetrical about the mean.

• It is skewed to the right.

• It is always bimodal.

• It has a mean of 1.

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CCSS.6.SP.A.3

In a standard normal distribution, what is the mean?

• 1

• 0

• 2

• Depends on the data

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CCSS.6.SP.A.3

What does a z-score represent?

• The total area under the curve

• The mean of the data

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

• The probability of a value

If the mean commuting time is 44 minutes with a standard deviation of 3.5, what is the z-score for a commuting time of 40 minutes?

• -0.14

• -1.14

• 1.14

• 0.14

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CCSS.HSS.ID.A.4

What is the probability that it takes less than 40 minutes to get to work if the z-score is -1.14?

• 0.6141

• 0.8729

• 0.1271

• 0.1190

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CCSS.HSS.ID.A.4

How do you find the probability of a value between two points using z-scores?

• Add the areas to the left of both z-scores

• Subtract the area to the left of the smaller z-score from the area to the left of the larger z-score

• Divide the area to the left of the larger z-score by the area to the left of the smaller z-score

• Multiply the z-scores

What is the z-score for a commuting time of 38 minutes if the mean is 44 minutes and the standard deviation is 3.5?

• -1.71

• 1.71

• -0.71

• 0.71

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CCSS.HSS.ID.A.4

What is the probability that it takes between 38 and 45 minutes to get to work?

• 0.5705

• 0.0436

• 0.6141

• 0.3859

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CCSS.HSS.ID.A.4

How do you find the probability of a value greater than a given point using z-scores?

• Divide the area to the left by the z-score

• Add the area to the left of the z-score to 1

• Subtract the area to the left of the z-score from 1

• Multiply the z-score by the area to the left

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CCSS.HSS.ID.A.4

What is the probability that it takes longer than 45 minutes to get to work if the z-score is 0.29?

• 0.8729

• 0.3859

• 0.1271

• 0.6141

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CCSS.HSS.ID.A.4