SOLUTION: Let X be the ratio of sales to profits of some company. Assume that X has distribution function F(x) = 0 if x<2, F(x) = (x^2-4)/5 if 2 < x < 3, F(x) = 1 if x>3. What is the probabi

Algebra ->  Probability-and-statistics -> SOLUTION: Let X be the ratio of sales to profits of some company. Assume that X has distribution function F(x) = 0 if x<2, F(x) = (x^2-4)/5 if 2 < x < 3, F(x) = 1 if x>3. What is the probabi      Log On


   

Question 1200764: Let X be the ratio of sales to profits of some company. Assume that X has distribution function F(x) = 0 if x<2, F(x) = (x^2-4)/5 if 2 < x < 3, F(x) = 1 if x>3. What is the probability that X is between 2.5 and 5?
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

In the post, the problem's formulation is incomplete.


To be complete, it must say that the distribution function is the CUMULATIVE distribution function, 
not the density distribution.


Therefore, I must to make this addition to clarify everything.


Also, the given fact that X is "the ratio of sales to profits of some company" is not necessary for the solution of the problem.


It is a typical "noise" to distract an attention of a reader.


To find the desired probability, simply take into account that F(5) = 1,

calculate F(2.5) = %282.5-4%29%5E2%2F4 = 0.5625  and compute the difference


    F(5) - F(2.5) = 1 - 0.5625 = 0.4375.



This number  0.4375  is your  ANSWER.

Solved.