The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function



$F(x) = \begin{cases} 1 - k x^{-3} \text{ for } x > 40000 \\ 0 \text{ otherwise,} \end{cases}$
for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals.

Part a)

Find the constant k here and provide its natural logarithm to three decimal places.

Natural logarithm of k:

Part b)

Calculate the mean salary given by the model.



Part c)

Find the proportion in the profession earning less than the mean, giving your answers as a fraction or to three decimal places.