Hear that, air?

An ideal gas of non-interacting helium atoms is in a thermal equilibrium at the temperature $T = 30^\circ \mbox{C}$. What's the probability that an atom in this gas has a speed near the speed of sound, i.e. has a speed in the range $340 \pm 5~\mbox{m/s}$ ?

Details and assumptions

• Mass of a helium atom is $6.646 \times 10^{-27}~\mbox{kg}$
• The probability density as a function of energy for an atom in an ideal gas is $p(E) = \frac{2}{kT\sqrt{\pi}} \sqrt{\frac{E}{kT}} \exp({-\frac{E}{kT}})$.
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