A study was conducted on the critical-part failures from 36 NASCAR races. The researchers discovered that the time in hours until the first critical-part failure is exponentially distributed with a mean of 0.5 hour. Find the probability that the time until the first critical-part failure is more than 2 hours.

1.83% probability that the time until the first critical-part failure is more than 2 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, we have that:

Find the probability that the time until the first critical-part failure is more than 2 hours.

1.83% probability that the time until the first critical-part failure is more than 2 hours.