Mall shoppers on average visit 3 stores in a 4hour shopping

Mall shoppers, on average, visit 3 stores in a 4-hour shopping time frame. We are interested in the probability that a randomly selected shopper will visit exactly 5 stores in a 6-hour shopping time frame.

1) Define the Random Variable (e.g. \"Let X = ....\")

2) Distribution, parameter(s) and support

3) Probability statement for this scenario

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

Mean is 3 stores in a 4-hour shopping time frame
Mean rate for 6 hour shopping time = 6*3/4 = 9/2 = 4.5
P( X = 5 ) = e ^-4.5 * 4.5^5 / 5! = 0.1708