Answered: Response time of fire-engines are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Response time of fire-engines are important. At a fire-station, the probability that your call
to a service line is answered in less than 15 seconds is 0.80. Assume that your calls are
independent.
(a) If you call 8 times, what is the probability that exactly 6 of your calls are answered
within 15 seconds?
(b) If you call 16 times, what is the probability that at most 12 calls are answered in less
than 15 seconds?
(d) What is the probability that you must call four times to obtain the first answer in less
than 15 seconds?
(e) What is the probability that you must call eight times for three of your calls to be
answered in less than 15 seconds?

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$G i v e n, p = 0.80 l e t X = n o . o f t i m e s p h o n e c a l l s a n s w e r e d X ~ B i n o m i a l (n, p) P (X = x) = (\begin{matrix} n \\ x \end{matrix}) p^{x} {(1 - p)}^{n - x}; x = 0, 1, 2, . . . . . n$

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