Recent homebuyers from a local developer allege that 30 of t

Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that will require substantial repairs. To test this allegation, we randomly sample 20 homes constructed by the developer and find that two of the homes did indeed have some major defect. If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20?

Solution

what is the probability of observing at most two defective homes out of a random sample of 20?

P ( x <= 2) = P(x=0) + P(x=1) + P(x=2)

P(x=0)= 20C0 * 0.30^0 * 0.70 ^(20-0) = 0.0007979

P(x=1)= 20C1 * 0.30^1 * 0.70 ^(20-1) = 0.006839

P(x=2)= 20C2 * 0.30^2 * 0.70 ^(20-2) = 0.02785

P( x <=2 ) = 0.0354869