Question

At a car manufacturing plant, 40% of cars have some sort of defect when they come off the line. If 12 inspectors randomly pick a car to check for defects, what is the probability 3, 4 , or 5 of them have defects

Answer 1

Sample size , n =    12
Probability of an event of interest, p =   0.4
  
Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P ( X = 3) = C (12,3) * 0.4^3 * ( 1 - 0.4)^9=      0.1419
P ( X = 4) = C (12,4) * 0.4^4 * ( 1 - 0.4)^8=      0.2128
P ( X = 5) = C (12,5) * 0.4^5 * ( 1 - 0.4)^7=      0.2270

the probability 3, 4 , or 5 of them have defects = P(X=3) + P(X=4) + P(X=5) = 0.5818