The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? (round to 3 decimal places)

0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

In which is the decay parameter.

The probability that x is lower or equal to a is given by:

Which has the following solution:

The probability of finding a value higher than x is:

In this question:

What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?

In which

So

0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

ratio is 2 : 9

the answer is three

13.5 : 3