Question

the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. what is the probability that a randomly selected part will fail in less than 20 hours

Answer 1

Using the exponential distribution, it is found that there is a 0.3297 = 32.97% probability that a randomly selected part will fail in less than 20 hours.

Exponential distribution

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

In this problem, the mean and the decay parameter are, respectively, given by:

$m = 50, \mu = \frac{1}{50} = 0.02$.

The probability that a randomly selected part will fail in less than 20 hours is given by:

$P(X \leq 20) = 1 - e^{-0.02 \times 20} = 0.3297$

0.3297 = 32.97% probability that a randomly selected part will fail in less than 20 hours.

More can be learned about the exponential distribution at brainly.com/question/18596455