Question

Let Z ∼ N(0, 1) be a standard normal random variable, and let z be a...

Let Z ∼ N(0, 1) be a standard normal random variable, and let z be a possible

value of Z. How large would z have to be to be considered an outlier by the 1.5 IQR rule?

Math   Statistics-And-Probability   
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Answer #1

The IQR for any data is calculated via the following formulla

Where Q1 is the first quartile ans Q3 is the third quartile of the data. It is readily calculated that for the standard normal distribution the first quartile is -.67 (using 0.2514 for 0.25) and the third quartile is .67. [Using standard normal table].

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Hence will be considered as the outlier in the data.

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