Substitute these values into the formula to get, \[Z=\frac{46.2-41.9}{6.7}=\frac{4.3}{6.7} \approx 0.64.\], Now turn to your z-score table. So there's gonna be some If you convert an individual value into a z-score, you can then find the probability of all values up to that value occurring in a normal distribution. That can sound bad at first, since it sounds like you got a 50% on the test, but it is simply telling you where you fall relative to all the other test-takers. In a z-distribution, z-scores tell you how many standard deviations away from the mean each value lies. Normal distributions are so useful because they are proportional to each other via the z-score and percentiles. How do you find the top 10 percent of a normal distribution? That is what the z-score formulas can help with. But exactly how long is that fish, in inches? That means the 10th percentile for Z is 1.28. In Step 3, you change the z-value back to an x-value (fish length in inches) using the z-formula solved for x; you get x = 16 + 1.28[4] = 10.88 inches. ","blurb":"","authors":[{"authorId":9121,"name":"Deborah J. Rumsey","slug":"deborah-j-rumsey","description":"

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. corresponding z-score. On a z-score table, the closest z-score to 80% is 0.84. So, a fish whose length is 1.28 standard deviations below the mean marks the bottom 10 percent of all fish lengths in the pond.\r\n\r\nBut exactly how long is that fish, in inches? For this, you will need the formula \[Z=\frac{x-\mu}{\sigma}.\], For this breed's growth chart, the mean is \(\mu =41.9\), the standard deviation is \(\sigma =6.7\), and the value \(x=46.2\). This represents the 10th percentile for X. about is the top 30% because that is who is going to be tested. AP.STATS: UNC1 (EU), UNC1.I (LO), UNC1.I.5 (EK) CCSS.Math: HSS.ID.A.4, HSS.ID.A. All kinds of variables in natural and social sciences are normally or approximately normally distributed. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9121"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"

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