Question

The length of time spent waiting in line at a certain bank is modeled by an exponential density function with a mean of 5 minutes. Find the probability that you would wait in line for at least 8 minutes in this bank.

Answer 1

`P(X >8)`

And for this case we can use the complement rule and we got:

`P(X >8)= 1-P(X<8)`

And we can use also the cumulative distribution function given by:

`F(x) =1 -e^(-\lambda x)`

And replacing we got:

`P(X >8)= 1-P(X<8)= 1- (1- e^{-(1)/(5) *8})= e^{-(1)/(5) *8} = 0.202`

Explanation:

For this case we can define the random variable of interest X as "The length of time spent waiting in line at a certain bank" and for this case we know that the distribution for X is given by:

`X \sim Exp(\lambda =(1)/(5))`

And for this case we want to find the following probability:

`P(X >8)`

And for this case we can use the complement rule and we got:

`P(X >8)= 1-P(X<8)`

And we can use also the cumulative distribution function given by:

`F(x) =1 -e^(-\lambda x)`

And replacing we got:

`P(X >8)= 1-P(X<8)= 1- (1- e^{-(1)/(5) *8})= e^{-(1)/(5) *8} = 0.202`