Presentation on theme: "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."— Presentation transcript:
1 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
2 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?
3 Standardized Scores (aka z-scores) Z-score represents the exact number of standard deviations a value, x, is from the mean.meanobservation (value)standard deviationExample: (test score problem)What would be the z-score for a student that received a 70 on the test?
4 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 =)
5 Z-scores are also called standardized scores. To calculate any z-score: 𝑧= 𝑥 − 𝑥 𝑠American 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?
6 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)
7 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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