The mean cost of domestic airfares in the United States rose to an all-time high of $380 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $100. a. What is the probability that a domestic airfare is $545 or more (to 4 decimals)? b. What is the probability that a domestic airfare is $265 or less (to 4 decimals)? c. What if the probability that a domestic airfare is between $300 and $490 (to 4 decimals)?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The mean cost of domestic airfares in the United States rose to an all-time high of $380 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are
a. What is the probability that a domestic airfare is $545 or more (to 4 decimals)?
b. What is the probability that a domestic airfare is $265 or less (to 4 decimals)?
c. What if the probability that a domestic airfare is between $300 and $490 (to 4 decimals)?
d. What is the cost for the 3% highest domestic airfares? (rounded to nearest dollar)
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