18. A salesperson has found that the probability of a sale on a single contact is approximately .03. If the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale? 19. Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that (a) no more than three customers arrive? (b) at least two customers arrive? (c) exactly four customers arrive? 20. (a) The random variable Y has a Poisson distribution and is such that P (Y = 0) = P (Y = 1). What is P (Y 2 = 1)? (b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during the call? 21. The mean number of automobiles entering a mountain tunnel per two-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation. Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three. Does the Poisson model seem reasonable for this problem? 22. The number of claims per month paid by an insurance company is modelled by a random variable N with p.m.f satisfying the relation p(n+1)= 13p(n), n=0,1,2,... where p(n) is the probability that n claims are filed during a given month (a) Find p(0). (b) Calculate the probability of at least one claim during a particular month given that there have been at most four claims during the month.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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18. A salesperson has found that the probability of a sale on a single contact is approximately .03. If the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale? 19. Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. During a given hour, what are the probabilities that (a) no more than three customers arrive? (b) at least two customers arrive? (c) exactly four customers arrive? 20. (a) The random variable Y has a Poisson distribution and is such that P (Y = 0) = P (Y = 1). What is P (Y 2 = 1)? (b) Cars arrive at a toll both according to a Poisson process with mean 80 cars per hour. If the attendant makes a one-minute phone call, what is the probability that at least 1 car arrives during the call? 21. The mean number of automobiles entering a mountain tunnel per two-minute period is one. An excessive number of cars entering the tunnel during a brief period of time produces a hazardous situation. Find the probability that the number of autos entering the tunnel during a two-minute period exceeds three. Does the Poisson model seem reasonable for this problem? 22. The number of claims per month paid by an insurance company is modelled by a random variable N with p.m.f satisfying the relation p(n+1)= 13p(n), n=0,1,2,... where p(n) is the probability that n claims are filed during a given month (a) Find p(0). (b) Calculate the probability of at least one claim during a particular month given that there have been at most four claims during the month.

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