20 of customers coming to a dealership will buy a car Assume

20% of customers coming to a dealership will buy a car. Assume customers are independent of each other. If 15 customers come in, we are interested in the probability at least 5 of them buy a car.

2) Distribution, parameter(s) and support

3) Probability statement for this scenario

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 15 4 ) * 0.2^4 * ( 1- 0.2 ) ^11 + ( 15 3 ) * 0.2^3 * ( 1- 0.2 ) ^12 + ( 15 2 ) * 0.2^2 * ( 1- 0.2 ) ^13 + ( 15 1 ) * 0.2^1 * ( 1- 0.2 ) ^14 + ( 15 0 ) * 0.2^0 * ( 1- 0.2 ) ^15   
= 0.836
P( X > = 5 ) = 1 - P( X < 5) = 0.164