Science:Math Exam Resources/Courses/MATH103/April 2010/Question 03 (a)
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Question 03 (a) 

A toxic chemical has been spilled somewhere on a 100 km stretch of highway. The probability that the spill occurred within km of the factory is shown in the panel below.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

What is the relation between the given cumulative function F(x) and the probability density function p(x)? 
Hint 2 

Since the Fundamental theorem of calculus says that Hence you are asked to plot the derivative of the given function F(x). 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The derivative p(x) is zero whenever F(x) is flat, and p(x) is positive whenever F(x) is increasing. 