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 25 minutes late.
​(b) It is 10 A.M. There is a 30​% probability the friend will arrive within how many​ minutes?

Answer 1

To find the probability that the friend is between 10 and 25 minutes late, we need to find the area under the curve between 10 and 25 on the x-axis.

The area under a uniform probability density function is given by: Area = base x height

where the base is the width of the interval (25-10 = 15 minutes) and the height is the value of the density function (1/30).

Therefore, the probability that the friend is between 10 and 25 minutes late is: Area = 15 x 1/30 = 0.5

Rounding to three decimal places, the probability is 0.500

So the answer is 0.500