75 of mall shoppers will stop to eat at the food court durin

75% of mall shoppers will stop to eat at the food court during their visit. Assume customers are independent of each other. At the start of the day, we are interested in the probability that the 6th shopper to walk past the food court will be first to stop by and eat.

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

2) Distribution, parameter(s) and support

3) Probability statement for this scenario

Solution

p = Prob for a mall shopper to eat at the food court = 0.75

Prob for 6th shopper to walk and eat

= Prob for first 5 shoppers did not walk and eat and 6th one to walk and eat

= (1-0.75)⁵(0.75)

= 0.25⁵(0.75)

= 0.0007323

1) X = 1,2.... is a Geometric variable

2) Geometric distribution with p = 0.75 and q = 0.25

3) P(X=x) = 0.25^x-1(0.75), x=1,2,,,,,