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Calculus Level 4

\[ \large \int_{-\infty}^{\infty} \left( \dfrac{e^{\frac{-x^2}{2}}}{\sqrt{2\pi}} \right) dx \]

If the value for the above integral is \(A\), find the value of \(b\) such that

\[ \large \int_{-b}^{b} \left( \dfrac{e^{\frac{-x^2}{2}}}{\sqrt{2\pi}} \right) dx = 0.9A \].

Give the answer to the nearest 3 decimal places.

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