Science:Math Exam Resources/Courses/MATH103/April 2010/Question 07 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q1 (f) • Q1 (g) • Q1 (h) • Q2 • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 •
Question 07 (b) 

The probability that a newly divided cell will divide again before t hours (where t ≥ 0) is given by (b) What is the probability that the cell will divide between 3 and 6 hours? (Leave your answer in terms of .) 
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 

If p(t) is the probability density function of a continuous random variable X, then the probability that an event happens is given by 
Hint 2 

How can you relate the given cumulative function F(t) to the probability density function p(t)? You don't need to calculate p(t) here if you use the Fundamental Theorem of Calculus. 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Again, let X be the continuous random variable that denotes the waiting time. Since we can use the Fundamental theorem of calculus to find the probability that the cell will divide between 3 and 6 hours: 