3. Suppose small aircraft arrive at a certain airport according to a Poisson process with rate 2 = 2 per20min,a. What is the probability that at most 2 small aircraft arrive during a 30-min period?b. What are the expected value and standarddeviation of the number of small aircraft that arriveduring 2-hr period?c. What is the probability that between 2 to 4 small aircraft arrive during a 90-min period?

Solution-: We find, (a) P[at most 2 small aircraft arrive during a 30 min period]=? (b) What are the…

Answered: 3. Suppose small aircraft arrive at a…

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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4. In the hour before noon, a busy corporation switchboard received an average of 55 calls. a. What is the probability that more than 70 calls will be received during this hour? b. What is the probability that fewer than 50 calls will be received during this hour? c. What is the probability that between 50 and 70 calls will be received during this hour? (Use the normal approx. to the Poisson distribution, without the continuity correction.
Suppose people immigrate into a territory at a Poisson rate of 2 per day. Assume that 40% of immigrants are adults and 60% are kids. a. What is the probability that 4 adult immigrants arrive in the next 3 days? b. What is the probability that the time elapsed between the arrival of 24th and the 25th kids is more than 2 days? c. Find mean and the variance of the time needed to have 50 adult immigrants in the territory.
1/ A company is going to release four quarterly reports this year. Suppose the company has a 35% chance of beating analyst expectations each quarter. a. What is the probability that the company beats analyst expectations every quarter of this year? b. What is the probability the company beats analyst expectations more than half the time this year? c. What is the expected number of times the company will beat analyst expectations this year?
Suppose weights, in pounds, of dogs in a city have an unknown distribution with mean 31and standard deviation 5 pounds. A sample of size n=39 is randomly taken from the population and the sum is taken. What is the probability that the resulting sum is between 1180 and 1194 pounds?
A category 4 hurricane strikes the U. S. mainland once every 4 years, on average,a) What are the expected value and standard deviation of the number of category 4 hurricanesthat will strike the U. S. mainland in the next century (100 years)?b) What is the probability that exactly 3 such hurricanes will strike the U. S. mainland in thenext 10 years?
The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.2 per minute between 7:00 P.M. and 10:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7:42 P.M. and 7:50 P.M. Interpret each result. (a) exactly eight (b) fewer than eight (c) at least eight
The number of hits to a website follows a Poisson process. Hits occur at the rate of 0.4 per minute between 7:00 P..M. and 9:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 7:21 P.M. and 7:25 P.M. Interpret each result. (a) exactly four (b) fewer than four (c) at least four ..... (a) P(4) =| (Round to four decimal places as needed.) On about of every 100 time intervals between 7:21 P.M. and 7:25 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (b) P(x<4) = (Round to four decimal places as needed.) On about of every 100 time intervals between 7:21 P.M. and 7:25 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (c) P(x24)=| (Round to four decimal places as needed.) hit(s). On about of every 100 time intervals between 7:21 P.M. and 7:25 P.M, the website will receive (Round to the nearest whole number as needed.) O Time Remaining: 03:54:41…
3. Football goal scoring events arrive as a Poisson process in a a 90-minute match at a mean rate of 2.7 goals per match. Find the probability that an interval time is less than 30 minutes: (A) 0.0672 (B) 0.4066 (C) 0.5934 (D) 0.9328
The times between arrivals in a queue follow an exponential distribution with a rate of 1. Check the incorrect alternative: a) 50% of arrivals will take place before 1 minute. b) If the times between arrivals are exponentially distributed with a rate equal to 1, then arrivals occur according to a Poisson distribution with an average equal to 1. c) Times between arrivals are independent. d) The variance of the times between arrivals is equal to 1. e) There is an average of one arrival every minute.
The time between arrivals of customers at the drive-up window of a bank follows an exponential distribution with a mean of 20 minutes. a)What is the probability that the arrival time between customers will be 13 minutes or less? b)What is the probability that the arrival time between customers will be between 13 and 27 minutes?
5. A new type of car tires is released on the market with rate of tire cracking: on average one crack every 2000km. (a) What is the probability that a randomly chosen tire will cover a distance of 500km without a single crack? (b) How many tires are expected to have two ore more cracks within a distance of 500km?
The number of hits to a website follows a Poisson process. Hits occur at the rate of 6.8 per minute between 7:00 P.M. and 11:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 10:13 P.M. and 10:14 P.M. Interpret each result. (a) exactly seven (b) fewer than seven (c) at least seven ..... (a) P(7) = (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (b) P(x <7)=| (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) (c) P(x27) = (Round to four decimal places as needed.) On about of every 100 time intervals between 10:13 P.M. and 10:14 P.M, the website will receive hit(s). (Round to the nearest whole number as needed.) Time Remaining:…

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