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Published byDante Culverson Modified over 3 years ago

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**Z-Scores are measurements of how far from the center (mean) a data value falls.**

Ex: A man who stands 71.5 inches tall is 1 standard deviation ABOVE the mean.(z-score = 1) Ex: A man who stands 64 inches tall is 2 standard deviations BELOW the mean. (z-score = -2) Adult Male Heights

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Based upon the Empirical Rule, we know the approximate percentage of data that falls between certain standard deviations on a normal distribution curve. Example: If a class of test scores has a mean of 65 and standard deviation of 9, then what percent of the students would have a grade below 56?

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**Standardized Scores (aka z-scores)**

Z-score represents the exact number of standard deviations a value, x, is from the mean. mean observation (value) standard deviation Example: (test score problem) What would be the z-score for a student that received a 70 on the test?

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**What is the z-score for a car that is traveling 60mph?**

Example: The mean speed of vehicles along a particular section of the highway is 67mph with a standard deviation of 4mph. What is the z-score for a car that is traveling at 72 mph? What is the z-score for a car that is traveling 60mph? Mark the z-scores on the number line below | | | | | | | (z =)

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**Z-scores are also called standardized scores. To calculate any z-score:**

𝑧= 𝑥 − 𝑥 𝑠 American Adult Males: mean of 69 inches and standard deviation of 2.5 inches. What is the standardized score for a male with a height of 72 inches? What is the standardized score for a male with a height of 62 inches?

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**To find the proportion or probability that a certain interval is possible, we use the z-score table.**

The z-score table always tells the proportion to the LEFT of that z-score value. What percentage of the data will have a z-score of less than 1.15? P(z < 1.15)

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Other Examples: Find P(z < 0.22) 2) Find P(z > 0.22) 3) Find P(0.22 < z < 1.15)

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