It is estimated that 45 of households own a riding lawn mowe

It is estimated that 45% of households own a riding lawn mower. A sample of 17 households is studied. What is the probability that no more than 3 of these own a riding lawn mower?

Solution

45% have the lawn mover , hence the probability = 0.45

probability of not having the lawn mover = 1-0.45 = 0.55

n =17

no more then 3 = p(0)+p(1)+p(2)+p(3)

p(0) = 17C0*(0.45)^0*(0.55)^17 = 0.00003

P(1) = 17C1*(0.45)^1*(0.55)^16 = 0.0005

P(2) = 17C2*(0.45)^2*(0.55)^15 = 0.0035

P(3) = 17C3*(0.45)^3*(0.55)^14= 0.014

HENCE PRONANILITY = TOTAL OF ABOVE = 0.01803