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z score

2009-11-22 7:05 am

As a general rule, an observation is considered an extreme value if its z score is less than 3, is it true ? In addition, The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, which mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the z-score for this observation ??
a) 18.750 b) 2.500 c)1.875 or d) 0.750

回答 (1)

用戶9112

2009-11-22 9:17 am

✔ 最佳答案

For normal distribution, most data will tend to lie in the middle portion of the distribution. The probability of a data decrease when it moves away from the centre. The probability of a data with corresponding z-score > 3, is 0.135% which is a very small number. Therefore an observation is considered extreme when its z-score is GREATER (not LESS) than 3.
For a population mean of 3.2 pounds and standard deviation 0.8 pound, if the sample size is 25 fishes, the standard deviation of the sample mean is 0.8/√25 = 0.16 pound.
When the sample mean is 3.6, the z-score is (3.6 - 3.2) / 0.16 = 2.5

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