Past exam of the physics A course of the University of Cambridge / 2014 / Paper 1 / Section A / 5 / Solution

Interpret the quoted r.m.s. as the root-mean-square fluctuation about the mean, namely the standard deviation $\sigma =10\mathrm{K}$. Standardization gives $z=(293-273)/10=2$. The supplied cumulative Gaussian curve gives $\Phi (2)\simeq 0.977$, henceThe exact Gaussian value is $0.02275$. A raw r.m.s. temperature of $10\mathrm{K}$ could not coexist with a mean of $273\mathrm{K}$; the spread interpretation is required.