Question

The life of an electric component has an exponential distribution with a mean of 8 years. What is the probability that a randomly selected one such component has a life less than 5 years? Answer: (round to 4 decimal places)

Answer 1

The probability is 0.4647

Explanation:

The variable X is the life of an electric component in years.

X follows a exponential distribution, it means that the probability that the life of an electric component is less than x years is calculated as:

`P(X<x)=1-e^{(-x)/(\beta ) }`

Where
`x\geq0` and
`\beta` is the mean life of the electric component.

So, replacing x by 5 and
`\beta` by 8, we get that the probability that a randomly selected component has a life less than 5 years is:

`P(X<5)=1-e^{(-5)/(8 ) }=0.4647`