Of all the new cars of a certain model that are sold 20 will

Of all the new cars of a certain model that are sold, 20% will require repairs done under warranty. A particular dealership sells 15 such vehicles.

(a) What is the probability that less than three of them will require repairs?

(b) Calculate the mean and the standard deviation for the distribution of X = number of vehicles that will require repairs.

n = 15

p = 0.2

P(X) = 15Cx(0.2)^x*(0.8)^(15-x)

a.) P(X<3) = P(0) + P(1) + P(2)

= (0.8)^15 + 15C1*(0.2)*(0.8)^14 + 15C2*(0.2)^2*(0.8)^13

= 0.398

b.) mean = np = 15*0.2 = 3

s.d = sqrt(np*(1-p)) = sqrt(15*0.2*0.8) = 1.55