Question

A website manager has noticed that during the evening? hours, about 3.5 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others and wants to model the time between purchases. Complete parts a through c. ?a) What model would you use to model the time between? events?

b) What is the mean time between? purchases?

?c) What is the probability that the time to the next purchase will be between 1 and 2? minutes?

Answer 1

(a) Time between events: Exponential Distribution

(b) Mean time between purchases = $\lambda$ = 3.5

(c)
Probability Density Function of Exponential Distribution is given bY;

$P(x)=\lambda e^{-\lambda x}$ ,

                              x > 0

           = 0, Otherwise

$P(1<x<2)=\int_{1}^{2}3.5 e^{-3.5x}dx$

$=-e^{-3.5x}$

between the limits 1 to 2.

Applying limits, we get:

$P(1<x<2)=0.0293$