Question

The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes. What is the probability that the service time:Is between 2 and 4 minutes?a. .2488b. .4493c. .2019d. .2474e. .1170

Answer 1

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 :-

$P(X\leq x)= 1-e^{-\frac{x}{\lambda}}$  

, where $\lambda$ = Mean of the distribution.

The probability that the service time is between 2 and 4 minutes will be :

$P(2\leq X \leq 4)=P(X\leq4)-P(X\leq 2)\\\\= (1-e^{\frac{-4}{2.5}})-(1-e^{\frac{-2}{2.5}})\\\\=e^{\frac{-2}{2.5}}-e^{\frac{-4}{2.5}}\\\\=0.449328964117-0.201896517995\\\\=0.247432446123\approx0.2474$

Hence, the correct option is d. .2474.