Answer: d. .2474.
Step-by-step explanation:
Given : The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.
The cumulative distribution function for exponential distribution is :-
[tex]P(X\leq x)= 1-e^{-\frac{x}{\lambda}}[/tex]
, where [tex]\lambda[/tex] = Mean of the distribution.
The probability that the service time is between 2 and 4 minutes will be :
[tex]P(2\leq X \leq 4)=P(X\leq4)-P(X\leq 2)\\\\= (1-e^{\frac{-4}{2.5}})-(1-e^{\frac{-2}{2.5}})\\\\=e^{\frac{-2}{2.5}}-e^{\frac{-4}{2.5}}\\\\=0.449328964117-0.201896517995\\\\=0.247432446123\approx0.2474[/tex]
Hence, the correct option is d. .2474.
