Of all the registered automobiles in a certain state, 35% violate the state emissions standard. Twelve automobiles are selected at random to undergo an emissions test. Find the probability that fewer than three of them violate the standard.
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Using the formula for the probability mass function of a binomial distribution, we have: \[ P(X = 0) = \binom{12}{0} \times 0.35^0 \times 0.65^{12} \] \[ P(X = 0) = 1 \times 1 \times 0.65^{12} \] \[ P(X = 0) \approx 0.0006 \] Show more…
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