Answer:
The probability is 0.4647
Step-by-step 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:
[tex]P(X<x)=1-e^{\frac{-x}{\beta } }[/tex]
Where [tex]x\geq0[/tex] and [tex]\beta[/tex] is the mean life of the electric component.
So, replacing x by 5 and [tex]\beta[/tex] by 8, we get that the probability that a randomly selected component has a life less than 5 years is:
[tex]P(X<5)=1-e^{\frac{-5}{8 } }=0.4647[/tex]
