●Example: The number of complaints that a dry-cleaning establishment receives per dayis a random variable having Poisson distribution with λ=3.3. Use the formula for aPoisson distribution to find the probability that it will receive only two complaints on anygiven day.

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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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In a recent year, a hospital had 4463 births. Find the mean number of births per day, then use that result and the Poisson distribution to find the probability that in a day there are 14 births. Does it appear likely that on any given day, there will be exactly 14 births?
The number of x people entering the intensive care unit (ICU) at a particular hospital on any givenday has a Poisson probability distribution with mean equal to five persons per day. What is the probabilitythat the number of people entering the ICU on particular fay is less than equal to two?
The number of calls received by an office follows Poisson distribution with a mean of 8 calls. What is the probability of receiving 5 calls in a day?
A bank received on average 9 bad cheques per day. What is the probability that the bank will receive 3 bad cheques on any given day. Hint: Use poisson distribution
A service counter employs one server who can serve 15 customers per hour. Customers arrive at the counter at the rate of 5 per hour. Both service rate and arrival rate follow a Poisson distribution. What is the probability that 4 customers are waiting in line? Round your answer to four decimals 2- A service counter employs one server who can serve 24 customers per hour. Customers arrive at the counter at the rate of 10 per hour. Both service rate and arrival rate follow a Poisson distribution. How much time, in minutes, does a customer, on average, spend in the system? Round your answer to one decimal.
The number of corner kicks in a 90 minute soccer game follows a Poisson distribution with a mean of 5. Then, the probability that there will be 3 corner kicks in 45 minutes is
The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page. What is the probability that the typist makes 3 errors on a page? What is the probability that a randomly selected page does not need to be retyped?
2. If electricity power failures occur according to a Poisson distribution with an average of 5 failures every 20 weeks, calculate the probability that there will not be more than one failure during a particular week.
4. A large insurance company indicates that 78% of the policy holders have at least one health issues and 22% do not health issues. Let Y1 be a random variable defined as Yı = 0, if the policy holder does not have any health issues; Yı = 1, if the if the policy holder have health issues. Write the probability distribution of Y1, E(Y1) and Var(Y1).

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-cleaning establishment receives per day is a random variable having Poisson distribution with 1-3.3. Use the formula for a Poisson distribution to find the probability that it will receive only two complaints on any given day.