The Normal Distribution · Superchallenge problem

The $1.5 \times \mathrm{IQR}$ rule flags a value as an outlier if it is below $Q_1 - 1.5\,\mathrm{IQR}$ or above $Q_3 + 1.5\,\mathrm{IQR}$. For a normal distribution, what fraction of all values does the rule flag? Use $z = 0.674$ for $Q_3$ and round to four decimal places.