For the purposes of constructing modified boxplots, outliers are defined as data values that are above $Q_{3}$ by an amount greater than $1.5 \times I \mathrm{QR}$ or below $\mathrm{Q}_{1}$ by an amount greater than $1.5 \times I \mathrm{QR}$, 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.

The probability that a randomly selected value taken from a normal distribution is considered an outlier is (Round to four decimal places as needed.)

Step 1 ：Define outliers as data values that are above \(Q_{3}\) by an amount greater than \(1.5 \times IQR\) or below \(Q_{1}\) by an amount greater than \(1.5 \times IQR\), where IQR is the interquartile range.

Step 2 ：Calculate the interquartile range (IQR) which is the range between the first quartile (\(Q_{1}\)) and the third quartile (\(Q_{3}\)). In a normal distribution, \(Q_{1}\) is the 25th percentile and \(Q_{3}\) is the 75th percentile.

Step 3 ：Use the Z-score to find these percentiles. The Z-score is a measure of how many standard deviations an element is from the mean. For a normal distribution, the Z-score for the 25th percentile is -0.674 and for the 75th percentile is 0.674.

Step 4 ：Calculate the IQR in terms of Z-scores, which is 0.674 - (-0.674) = 1.348.

Step 5 ：Define an outlier as a value that is more than \(1.5 \times IQR\) away from \(Q_{1}\) or \(Q_{3}\). In terms of Z-scores, this is a value that is more than \(1.5 \times 1.348 = 2.022\) standard deviations away from the mean.

Step 6 ：Find the probability that a value is more than 2.022 standard deviations away from the mean in a normal distribution. This is the same as finding the area under the curve of the normal distribution outside of -2.022 and 2.022.

Step 7 ：Use the cumulative distribution function (CDF) of the normal distribution to find this area. The CDF gives the probability that a random variable is less than or equal to a certain value. So, to find the probability that a value is more than 2.022, subtract the CDF of 2.022 from 1.

Step 8 ：To find the probability that a value is less than -2.022, find the CDF of -2.022.

Step 9 ：The total probability of being an outlier is the sum of these two probabilities, which is approximately 0.0432.

Step 10 ：Final Answer: The probability that a randomly selected value taken from a normal distribution is considered an outlier is approximately \(\boxed{0.0432}\).