A local politician claims that 1 in 5 automobile accidents involve a teenage driver. He is advocating increasing the age at which teenagers can drive alone. Over a 2 month period, there are 67 accidents in your city, and only 9 of them involve a teenage driver. If the politician is correct, what is the chance that you would have observed 9 or less accidents involving teenagers?

Question

A local politician claims that 1 in 5 automobile accidents involve a teenage driver.  He is advocating increasing the age at which teenagers can drive alone.  Over a 2 month period, there are 67 accidents in your city, and only 9 of them involve a teenage driver.  If the politician is correct, what is the chance that you would have observed 9 or less accidents involving teenagers?

I have the correct answer, it's 0.0524, but I don't understand how to get this answer.  Please help.  (I would like to know how to do this by hand and also using a TI-84 calculator)

Thanks in advance.

Reiny · Answer

Prob(9 or less accidents involving teenagers)
= P(1 teenager involved) + P(2 teens involved) + ...+ P(9teens involved)
or
= 1 - P(no teen involved in 9 accidents)

Now when you say, "If the politician is correct" I will assume that we should use his/her data, and we would get.
Prob(teen involved) = .2
prob(no teen involved) = .8

P(as stated) = 1 - .8^9 = .86578

IF we use the actual data
P(teen involved) = 9/67 = .134328
P(no teen involved) = 58/67 = .865672 , (note they a add up to 1)

Prob(as stated) = 1 - (58/67)^9 = .72699

Somehow I think that I misunderstand the question