The annual salaries (in $) within a certain profession are modelled by a random variable with the cumulative distribution function-3F(x) =(1 − kx¯³ for x > 400000 otherwise,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.☐

Part a) Find the constant kThe problem gives us a function that describes how salaries are…

Answered: The annual salaries (in $) within a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An article in the European Physical Journal B ["Evidence for the exponential distribution of income in the USA" (2001, Vol. 20, pp. 585- 589)] shows that individual income in the US can be approximated with an exponential distribution. Suppose that the mean of individual income in a year is $25000. eTextbook and Media (b) What percentage of individuals in the US earn less than $20000? Round your answer to three decimal places (e.g. 0.987). P(X 50000) = (d) What is the income exceeded by 1% of individuals? Round your answer to the nearest integer (e.g. 9876). x =
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