Thirty percent of all customers who enter a store will make

Thirty percent of all customers who enter a store will make a purchase. Suppose that
6 customers enter the store and that these customers make independent purchased decisions. Let Xdenote the total number of the six customers who will NOT make a purchase. Indentify the two parameters of the binomial distribution.

Find out the mean of the X.

Find out the variance of X.

Find out the probability that all customers make a purchase.

Solution

70% do not make purchases. p =0.7, n=6

mean of X =np = 0.7*6 = 4.2

variance = n*p*(1-p) = 0.7*6*0.3 = 1.26

P(x=0) = 0.3^6 = 0.000729