Question 1 Uniform Probability Distribution (60 – 70 mins) Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. 1. Give a mathematical expression for the probability density function of flight time and the expected value and variance of the distribution; 2. Create a scatter graph using dynamic process learnt in the previous sessions to show the uniform probability distribution graphically, then answer the below questions: a. What is the probability that the flight will be no more than 5 minutes late? b. What is the probability that the flight will be more than 10 minutes late? c. What is the probability that the flight will be between 4 and 8 minutes late? d. In a month of 200 flight journeys finished, how many should have arrived 5 minutes or less earlier?
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!
Question 1 Uniform Probability Distribution (60 – 70 mins) Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. 1. Give a mathematical expression for the probability density
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