For the purposes of constructing modified boxplots, outliers are defined as data values that are above Q3 by an amount greater than 1.5IQR or below Q1 by an amount greater than 1.5IQR , where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.

Question

Mathematics

Connor Mack

1 March, 18:00

For the purposes of constructing modified boxplots, outliers are defined as data values that are above Q3 by an amount greater than 1.5IQR or below Q1 by an amount greater than 1.5IQR , where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, it is an outlier.

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Maximilian Hensley · Answer 1

0.0602

Step-by-step explanation:

Given that a value is randomly selected from a normal distribution at random.

To find the probability that the value is an outlier

Z score (std) for Q1 = 0.675 and Q3 = =0.675

IQR = 1.250

1.5xIQR = 1.875

P (outlier) = P (Z1.875)

=2 (0.5-0.4699)

= 0.0602