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

Answer:

$P(X >8)$

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:

$P(X >8)= 1-P(X<8)= 1- (1- e^{-\frac{1}{5} *8})= e^{-\frac{1}{5} *8} = 0.202$

Step-by-step 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:

$X \sim Exp(\lambda =\frac{1}{5})$

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:

$P(X >8)= 1-P(X<8)= 1- (1- e^{-\frac{1}{5} *8})= e^{-\frac{1}{5} *8} = 0.202$