(a) The probability that a molecule in the atmosphere is at a height between z and z + dz above the surface of the Earth isproportional to e-z/A dz (capital Greek lambda). Determine the constant of proportionality. Sketch this distribution.(b) What is the mean molecular height, i.e. the mean height of a molecule?(c) What is the variance in the molecular height?(d) What is the standard deviation in the molecular height?

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(a) The probability that a molecule in the atmosphere is at a height between z and z + dz above the surface of the Earth is proportional to e-z/^ dz (capital Greek lambda). Determine the constant of proportionality. Sketch this distribution.