Question

The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the probability that a randomly selected one such component has a life more than 8 years? Answer: (Round to 4 decimal places.)

Answer 1

Answer:

$P(X>8)$

And for this case we can use the cumulative distribution function given by:

$F(x) = 1- e^{-\lambda x}$

And if we use this formula we got:

$P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070$

Step-by-step explanation:

For this case we can define the random variable of interest as: "The life of an electric component " and we know the distribution for X given by:

$X \sim exp (\lambda =\frac{1}{8.9})$

And we want to find the following probability:

$P(X>8)$

And for this case we can use the cumulative distribution function given by:

$F(x) = 1- e^{-\lambda x}$

And if we use this formula we got:

$P(X>8)= 1- P(X \leq 8) = 1-F(8) = 1- (1- e^{-\frac{1}{8.9} *8})=e^{-\frac{1}{8.9} *8}= 0.4070$