23. In Fall 2022, the Loyola University Chicago Math Department will hold a competition to see who can give the longest

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23 In Fall 2022 The Loyola University Chicago Math Department Will Hold A Competition To See Who Can Give The Longest 1 (57.21 KiB) Viewed 30 times

23. In Fall 2022, the Loyola University Chicago Math Department will hold a competition to see who can give the longest lecture. Let x represent the length of the lecture in hours. Because we want this competition to (eventually) end, it is decided that the competition will end after 9 hours (if anyone is still teaching). The Professor that either lasts the longest or any Professor who reaches 9 hours will be declared the victor. The (probability) density function for x is given below 3 3 < 0 22 p(:) 29 2+ 18 9 0 0<<9 2 > 9 (a) What is the mean lecture time? Round your answer to 2 decimal places if neces- sary (b) What proportion of Professors' lectures are between 1 and 2 hours? Round your answer to 3 decimal places if necessary (c) Find the formula of the cubic function whose solution between 0 and 9 is the median of x. You do not need to solve the cubic function or find the solution itself, only give the formula