The number of accidents in a certain city is modeled by a Poisson random variable with an average rate of3 accidents per day. Suppose that the number of accidents on different days are independent. Use thecentral limit theorem to find the probability that there will be more than 100 accidents in a certain month.Assume that there are 30days in a month.

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Answered: The number of accidents in a certain…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A bakery produces an average of 50 loaves of bread per day. The number of loaves produced by the bakery follows a Poisson distribution. What is the probability that the bakery will sell at least two loaves of bread in a day? Explain each step along with the computation.
A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentages of fishermen who caught x fish in a 6-hour period while fishing from shore. A) Find the probability that a fisherman selected at random fishing from shore catches one or more fish in a 6-hour period. B) Find the probability that a fisherman selected at random fishing from shore catches two or more fish in a 6-hour period. C) Compute ?, the expected value of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4). D) Compute ?, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round "at least 4" to 4).
The time between busses on Stevens Creek Blvd is 12 minutes. Therefore the wait time of a passenger who arrives randomly at a bus stop is uniformly distributed between 0 and 12 minutes. Find the probability that a person randomly arriving at the bus stop to wait for the bus has a wait time of at most 5 minutes.
The number of forklift topples in an area follows a poisson-process with rate 3 accidents per week. Suppose that we observed one forklift topple in the first week. What is the probability that we will observe at most one forklift topples in the next 2 days?
There is a bus coming to a bus stop every 10 minutes. The waiting time of any person at the stop is a random variable with a continuous uniform distribution. What is the probability that the waiting time is at most two minutes?
The time to fly between New York City and Chicago is uniformly distributed with a minimum of 56 minutes and a maximum of 100 minutes. What is the probability that a flight is less than 63 minutes?
Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes. The probability is 0.0905 (Round to four decimal places as needed.)
Suppose that the amount of time it takes a clerk to process an employment application is uniformly distributed between 5 and 12 minutes. What is the probability that the clerk will take exactly 7 minutes to process a randomly selected application?

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