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

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x