The potholes on a major highway in the city of Chicago occur at the rate of 3.4 per mile

Question

The potholes on a major highway in the city of Chicago occur at the rate of 3.4 per mile. Compute the probability that the number of potholes over 3 miles of randomly selected highway is

a. exactly seven.
b. fewer than seven.
c. at least seven.

Answer 1

Hi Thuy,

 

This is a proportion or ratio problem.  You could set this up as fractions and cross-multiply, but this is rather simple, especially since you don't need an exact answer.

 

So, just thinking logically (and rounding) ... If there are 3 potholes in a mile, in 3 miles there would be 3 times 3 (9).  So, we know there are more than 9, and you're done.

 

 

Now, here's how you would do it mathematically to get a precise answer:

  - Set up as fractions equal to each other.
  - Be very careful where you put the x (the unknown)
  - Cross-multiply to solve.
So our formula is 3.4/1 = x/3
When we cross-multiply we get 1x = 3.4 X 3 … x = 10.2

 

I hope that helps with this problem and all similar questions.

 

Paul L.