6.3 (10 points) In a company there are 7000 employees and 2000 of them have been
ID: 3233373 • Letter: 6
Question
6.3 (10 points) In a company there are 7000 employees and 2000 of them have been with the company for less than 3 years. The salary of an employee is uniformly dis- tributed between $50; 000 and $70; 000 if the employee has been with the com- pany for less than 3 years and is instead uniformly distributed between $60; 000 and $100; 000 if the employee has been with the company for 3 years or longer.
If you know that Mr. Smith's salary is between $60; 000 and $70; 000 what is the probability that Mr. Smith has been with the company for less than 3 years?
1 If you know that Mr. White's salary is between $65; 000 and $75; 000 what is the probability that Mr. White has been with the company for less than 3 years?
If you know that Mr. Green's salary is between $65; 000 and $75; 000 what is the probability that Mr.Green has been with the company for less than 3 years?
Explanation / Answer
P($60,000 to $70,000 salary for someone who has been with the company for less than 3 years)
= (70,000-60,000)/(70,000-50,000)
= 1/2
P($60,000 to $70,000 salary for someone who has been with the company for more than 3 years)
= ((70,000-60,000)/(100,000 - 60,000)
= 1/4
P(less than 3 years | salary between $60,000 and $70,000) = P(less than 3 years and salary between $60,000 and $70,000)/P(salary is between $60,000 and $70,000)
= (2000/7000)x1/2/((2/7 x 1/2) + (5/7 x 1/4))
= 0.4444
If you know that Mr. Smith's salary is between $60,000 and $70,000 the probability that Mr. Smith has been with the company for less than 3 years = 0.4444
_______________________________________________________________________________________________
P($65,000 to $75,000 salary for someone who has been with the company for less than 3 years)
= (70,000-65,000)/(70,000-50,000)
= 1/4
P($65,000 to $75,000 salary for someone who has been with the company for more than 3 years)
= ((75,000-65,000)/(100,000 - 60,000)
= 1/4
P(less than 3 years | salary between $65,000 and $75,000) = P(less than 3 years and salary between $65,000 and $75,000)/P(salary is between $65,000 and $75,000)
= (2/7)x1/4 / ((2/7 x 1/4) + (5/7 x 1/4))
= 2/7
=0.2857
If you know that Mr. White's salary is between $65,000 and $75,000 the probability that Mr. White has been with the company for less than 3 years = 0.2857
If you know that Mr. Green's salary is between $65,000 and $75,000 the probability that Mr. Green has been with the company for less than 3 years = 0.2857
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