An automatic machine produces on average, 10% of its components outside of the tolerance required. In a sample of 10 components from this machine, determine the probability of having two components outside of the tolerance required by assuming a binomial distribution.

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Debye Theory of Solids

In solid-state physics, debye theory is used to estimate the phonons contributing to the specific heat capacity in a solid. It explains that the specific heat is a consequence of the vibrations of the atomic lattice of the solid, which is in contrast to the Einstein model. In the Einstein model, solids are treated as independent, non-interacting quantum harmonic oscillators. This model clearly explains the low-temperature dependence of the heat capacity, which is proportional to T3. This is known as Debye T3 law.