A local politician claims that one in five automobile accidents involve a teenage driver. He is advocating increasing the age at which teenagers can drive alone. Over a two-month period there are 67 accidents in your city, and only nine of them involve a teenage driver. If the politician is correct, what is the chance that you would observe nine or fewer accidents involving a teenage driver?
A)about 0.05
B)about 0.09
C)about 0.16
D)about 0.11

Question

Quizplus · Accepted Answer

The probability of observing nine or fewer accidents involving a teenage driver, given the politician's claim, can be calculated using the binomial distribution formula or a binomial probability table. The politician claims that one in five accidents involve a teenage driver, which means the probability of an accident involving a teenage driver is 0.2 (or 20%). Given 67 accidents, the probability of observing 9 or fewer accidents involving a teenage driver is about 0.09, according to binomial distribution calculations. This calculation involves summing the probabilities of observing 0, 1, 2, ..., 9 accidents involving teenage drivers out of 67 total accidents, each with a success probability of 0.2.

A Local Politician Claims That One in Five Automobile Accidents