Of all the new vehicles of a certain model that are sold 11

Of all the new vehicles of a certain model that are sold, 11% require repairs to be done under warranty during the first year of service. A particular dealership sells 20 such vehicles. What is the probability that fewer than 3 of them require warranty repairs? Round your answer to four decimal places.

Solution

This is binomial.

n = 20, p = .11, x is fewer than 3, (0, 1, or 2)

P(X = x) = nCx*p^x*(1-p)^(n-x)

P(X = 0) = 20C0*.11^0*.89^20 = 0.0972

P(X = 1) = 20C1*.11^1*.89^19 = 0.2403

P(X = 2) = 20C2*.11^2*.89^18 = 0.2822

P(X = 0, 1, or 2) = .0972 + .2403 + .2822

= 0.6198 (answer)

(note this can also be done on a calcultor using binomcdf(20, .11, 2))