The time in hours required to repair a machine is an exponential distributed random variable with the average repair time of 2 hours, what is the probability that the repair time takes between 2 to 4 hours

0.4968 = 49.68% probability that the repair time takes between 2 to 4 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:

Average repair time of 2 hours

This means that

What is the probability that the repair time takes between 2 to 4 hours

More than 2:

Less than 4:

Between two and four:

0.4968 = 49.68% probability that the repair time takes between 2 to 4 hours

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).