1. For commercial flights in 2009, approximately 90% arrived on time (within 15 minutes of scheduled arrival time). Complete parts a through c below.
a. Assuming that this success rate still holds, if you randomly select five flight and assume they are independent, what is the probability that all will arrive on time?
The probability that all five will arrive on time is____________.
Round answer to three decimal places as needed.
b. What is the probability that at least one of the flights will be late?
Round answer to three decimal places as needed.
c. If all five flights are on the same day in December and all five flights to the same city, explain why the binomial model is not appropriate for finding the probability that at least one flight will be late.
Choose the correct answer below.
A. The flights might not be independent, because the weather could be bad and that might cause most of the flights to be late. Thus, if one flight is late, the others are more likely to be late.
B. The number of outcomes is greater than two, since flights could be either on time, late due to the bad weather or late because the flights ahead of it were delayed due to bad weather.
C. The number of flights is not fixed, because some flights might need to make emergency landings and never arrive due to bad weather.
2. According to a traffic safety administration organisation, the rate of seat belt use i a certain country for 2009 was 84%. Suppose that you looked at two people, selected randomly and independently from the population, to see weather each had his or her seat belt fastened in 2009.
A. What is the probability that neither person had her or his belt fastened?
P(Neither fastened)=_________ (round to four decimal places as needed)
B. What is the probability that at least one person had her or his belt fastened? (Hint: "At least on had the belt fastened" is the complement of "neither one had the belt fastened."
P(At least one fastened)=_________ (Round to four decimal places as needed)