Question 1

(a) Two airlines, Airline X and Airline Y, both offer flights between two cities. The airlines compete on price, convenience, and other factors that affect the demand for their flights. Over several recent months, the proportion of time that each airline sold approximately 100, 200 and 300 tickets per day was recorded and is presented in the following joint probability table:

		X
		100	200	300
Y	100	0.05	0.20	0.05
	200	0.15	0.25	0.10
	300	0.05	0.10	0.05

1. Which airline expects to sell the most tickets, on average? Show your work.

1. Are the two airlines' ticket sales statistically independent?

(b) The time taken for a university student to complete an online quiz is normally distributed with a mean () of 30 minutes and a standard deviation () of 5 minutes.

1. What is the probability that a student will take between 20 and 40 minutes to complete the quiz? Show your work.

1. What is the probability that a student will take more than 45 minutes to complete the quiz? Show your work.