4. Students arrive at a tutoring center to a Poisson process with a rate of 10 per hour.(a) What is the probability that the second arrival is observed less than 15 minutes after the firstarrival?(b) What is the probability that the third arrival is observed less than 10 minutes after the secondarrival if it has not yet been observed 5 minutes after the second arrival?(c) What is the probability that more than 20 minutes is required for the third arrival?(d) Suppose a volunteer working at the center has a 6-hour shift. Compute the expected value andthe variance for the number of students who would arrive during her shift.

Answered: Image /qna-images/answer/3ab0aada-0078-4711-8dba-029c92b1136d.jpg

Answered: 4. Students arrive at a tutoring center…

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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2) The number of x people entering the intensive care unit (ICU) at a particular hospital on any given day has a Poisson probability distribution with mean rate of five persons per day. What is the probability that the number of people entering the ICU for 5 days is between 20 and 35 inclusive?
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.
A bus company is interested in the wait time of its passengers between 8:00 AM and 8:00 PM. Suppose that the wait time follows a uniform distribution with the minimum wait time being one minute and the maximum wait time of 10 minutes. (a) What is the probability that a passenger will wait between 5 and 10 minutes? (b) What is the probability that a passenger will wait for 10 minutes?
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?
"Philippine General Hospital (PGH) anguish about queue in emergency rooms. The medical staff on hand cannot accommodate the patient on-queue if there are more than 10 emergency cases in a given hour. It is assumed that patient arrival follows a Poisson process, and historical data suggest that, on the average, 10 emergencies arrive per hour. What is th emergencies arrive during a 4-hour shift?" probability that more than 25
Philippine General Hospital (PGH) anguish about queue in emergency rooms. The medical staff on hand cannot accommodate the patient on-queue if there are more than 10 emergency cases in a given hour. It is assumed that patient arrival follows a Poisson process, and historical data suggest that, on the average, 8 emergencies arrive per hour. What is the probability that more than 25 emergencies arrive during a 2-hour shift?"
1. Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour. Suppose that you exit the workplace at 6:00 p.m. Determine the following: (a) Probability that 3 cabs pass by 6:30 p.m. (b) The expected number of cabs that pass by 6:10 (c) Probability that you wait more than 10 minutes for a cab.
1. Strikes in a factory occur according to a Poisson process at a mean rate of 2 per year (we assume a year to be exactly 52 weeks). (a) Find the probability that there is exactly one strike in the first 4 weeks and exactly 3 strikes in the subsequent 13 weeks. (b) What is the probability that at least 2 strikes occur in 13 weeks? (c) How many strikes are expected to occur in 2 years?

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