Question 1 Uniform Probability Distribution (60 – 70 mins) Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights fromCincinnati to Tampa. Suppose we believe that actual flight times are uniformlydistributed 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 5minutes 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 8minutes late?d. In a month of 200 flight journeys finished, how many should have arrived 5 minutes or less earlier? Question 2 Normal DistributionNew York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55. 2 a. Draw on a piece of paper the Normal Distribution curve and mark the Mean and 1 unit standard deviation to each side of the Mean. 2 b. Show the Probability Density Function to your tutor and point it on your graph.
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