a. Explanation Given info: In a study of “Ship-to-shore transfer times”, to estimate the ship-to-shore transfer times the researchers used an exponential distribution to model the time between arrivals of the smaller craft at the pier. The mean arrival time is 17 minutes. Calculation: Exponential Distribution: A random variable X is said to follow Exponential distribution if the density function of X is, f ( x ) = 1 θ e − x θ , ( x > 0 , θ > 0 ) . Where the mean is μ = θ and the standard deviation is σ = θ . The mean time between arrivals at the pier is 17 minutes. Thus, the random variable X , the time between arrivals of the smaller craft at the pier, follows exponential distribution with μ = 17 and the probability distribution is, f ( x ) = e − x 17 17 , ( x > 0 ) Now, for different values of X the probability value of X is, X f ( x ) = e − x 17 17 1 f ( 1 ) = e − 1 17 17 = 0.0555 3 f ( 3 ) = e − 3 17 17 = 0 b. To determine To find: The probability that the second craft will arrive at the unloading zone and have to wait before docking.

13th Edition

ISBN: 9780134080215

Author: James T. McClave, Terry T Sincich

Publisher: PEARSON

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Chapter 5.6, Problem 111ACI

To determine

To graph: The distribution.

To determine

To find: The probability that the second craft will arrive at the unloading zone and have to wait before docking.

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Chapter 5.6, Problem 110ACI

Chapter 5.6, Problem 112ACI

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Chapter 5 Solutions

Statistics (13th Edition)

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