Question

The graph to the right is the uniform probability density function for a friend who is x minutes late:

​(a) Find the probability that the friend is between 10 and 30 minutes late.

​(b) It is 10 A.M. and there is a 20​% probability the friend will arrive within how many​ minutes?

Answer 1

Answer for (a): 2/3

Step-by-step explanation:
In a uniform distribution, all probabilities are equal. In this case, the probability for being ‘x’ minutes late is each 1/30. Therefore, the probability that the friend is between 10 and 30 minutes late is 20/30 because we exclude the first 10 minutes. That can be simplified down to 2/3.

Answer for (b): 6 minutes

Step-by-step explanation:
The answer is simply 20% of 30. Since 30x0.2 is 6, the friend will arrive within 6 minutes.