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.

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^{-(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^{(-4)/(2.5)})-(1-e^{(-2)/(2.5)})\\\\=e^{(-2)/(2.5)}-e^{(-4)/(2.5)}\\\\=0.449328964117-0.201896517995\\\\=0.247432446123\approx0.2474`

Hence, the correct option is d. .2474.