A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. 0 sxs 2 f(x) = otherwise (a) Find the value of k. (Enter your answer to three decimal places.) Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.] f(x) f(x) 1.5 1.5 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 f(x) f(x) 1.5 1.5 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 (b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.) (c) What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 105 sec beyond the end of the hour? (Round your answer to four decimal places.)

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. 0 sxs 2 f(x) = otherwise (a) Find the value of k. (Enter your answer to three decimal places.) Draw the corresponding density curve. [Hint: Total area under the graph of f(x) is 1.] f(x) f(x) 1.5 1.5 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 f(x) f(x) 1.5 1.5 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0 (b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.) (c) What is the probability that the lecture continues beyond the hour for between 60 and 90 sec? (Round your answer to four decimal places.) (d) What is the probability that the lecture continues for at least 105 sec beyond the end of the hour? (Round your answer to four decimal places.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.6: Exponential And Logarithmic Equations

Problem 64E

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