### Probability Distributions: Parking Tickets Issuance#### Problem 5:Tina is a traffic warden. The number of parking tickets she issues per day, from Monday to Saturday inclusive, may be modelled by a Poisson distribution with a mean of 11.5. By using suitable approximating distributions, find:(i) The probability that on a particular Tuesday she issues at least 15 parking tickets.(ii) The probability that during any week (excluding Sunday) she issues at least 50 parking tickets.(iii) The probability that during four consecutive weeks she issues:(a) At least 50 parking tickets each week.(b) At least 200 parking tickets altogether.**Note:** You must account for the difference in the two answers. ---These problems require an understanding of the Poisson distribution and approximation techniques commonly used in probability theory and statistics. 1. **Poisson Distribution**: This is a probability distribution that models the number of events occurring within a fixed interval of time or space.2. **Approximations**: For large sample sizes or specific conditions, different approximations (such as normal or binomial approximations) might be employed to simplify the calculations.The steps involved in solving these problems typically include determining the mean and variance of the distribution, identifying the appropriate approximation, and then using statistical techniques or tools to find the required probabilities.

Name: ### Probability Distributions: Parking Tickets Issuance#### Problem 5
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: ### Probability Distributions: Parking Tickets Issuance#### Problem 5:Tina is a traffic warden. The number of parking tickets she issues per day, from Monday to Saturday inclusive, may be modelled by a Poisson distribution with a mean of 11.5. By us

The mean of the parking issued from Monday to Saturday is 11.5

Math

Probability

5 Tina is a traffic warden. The number of parking tickets she issues per day, from Monday to Saturday inclusive, may be modelled by a Poisson distribution with mean 11.5. By using suitable approximating distributions, find (i) the probability that on a particular Tuesday she issues at least 15 parking tickets (ii) the probability that during any week (excluding Sunday) she issues at least 50 parking tickets (iii) the probability that during four consecutive weeks she issues (a) at least 50 parking tickets each week (b) at least 200 parking tickets altogether. Account for the difference in the two answers.

5 Tina is a traffic warden. The number of parking tickets she issues per day, from Monday to Saturday inclusive, may be modelled by a Poisson distribution with mean 11.5. By using suitable approximating distributions, find (i) the probability that on a particular Tuesday she issues at least 15 parking tickets (ii) the probability that during any week (excluding Sunday) she issues at least 50 parking tickets (iii) the probability that during four consecutive weeks she issues (a) at least 50 parking tickets each week (b) at least 200 parking tickets altogether. Account for the difference in the two answers.

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...

See similar textbooks

Related questions

Q: what is the probability that exactly one is a shutout?

A: The number of runs scored by a certain baseball team per game follows a Poisson distribution with A…

Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

Q: 6. In a certain communications system, there is an average of 1.3 transmission errors per 10…

A: The frequency distribution broadly classified as observed frequency distribution and theoretical…

Q: probability that there will be exactly two accidents at the intersection during a week?

A: The number of accidents per day at a busy intersection has a Poisson distribution with mean 0.5…

Q: ow a Poisson distribution, with a n of 2.5 work-related injuries a h. What is the probability that…

A: Given:λ = mean=2.5x = Number of injuries occur. For the first case, there is not injury means x=0.…

Q: The number of earthquakes that occur per week 1.5. follows a Poisson distribution with a mean of (a)…

A: Introduction: It is required to obtain the Poisson probabilities using manual calculation, and R…

Q: Assume that the number of students in a class follows the Poisson distribution with λ = 14. The…

A: Poisson distribution is a discrete probability distribution.

Q: For Monday through Thursday when there isn't a holiday, the average number of vehicles that visit a…

A: Poisson distribution is an average of 9 minutes P(X =λ ) =e-λλxx! x = 0,1,2,........ λ=9

Q: (a) Let X be the number of times you swim in a given week when you have visited the gym on 4…

A: You go to the ARC gym 4 times a week, each time you visit there is a 0.85 probability that you will…

Q: The number of accidents per day at a busy intersection has a Poisson distribution with mean 0.4…

A: The number of accidents per day at a busy intersection has a Poisson distribution with mean 0.4…

Q: The number of days Anum makes use of public transport for travelling from Rawalpindi to Islamabad…

A: Given: Mean (λ) = 6 Consider, X be a random variable that represents the number of days Anum uses…

Q: In a recent year, a hospital had 4472 births. Find the mean number of births per day, then use…

Q: In a recent year, a hospital had 4395 births. Find the mean number of births per day, then use…

A: Given,no.of births per year =4395no.of days per year =365

Q: In a recent year, a hospital had 4350 births. Find the mean number of births per day, then use…

A: Given that, a hospital had 4350 births in a recent year Here, consider the year has non-leap year…

Q: l Canadian adults have used their cell phone while in a retail store. I drive down to the local…

A: The sampling distribution of the sample proportion is approximately normal with at least 5 expected…

Q: Data from the Central Hudson Laboratory determined that the mean number of insect fragments in…

A: Given Information: In a 27-gram bar the mean number of insect fragments would then be 1.73. Assume…

Q: 5 Tina is a traffic warden. The number of parking tickets she issues per day, fro Monday to Saturday…

A: X= Number of parking tickets Tina issues per day X~Poisson(11.5) (i) Using Excel function…

Q: The number of typing errors made by a typist has a Poisson distribution with an average of three and…

A: It is given that, the number of typing errors made by a typist has a Poisson distribution with an…

Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

A: We use Poisson distribution if the probability of success of an event is very small. If X is a…

Q: The number of people arriving per hour at the emergency room (ER) of a local hospital seeking…

A: NOTE-AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION ONLY Here Given The number of people…

Q: In a recent year, a hospital had 4384 births. Find the mean number of births per day, then use…

A: Given that, The hospital had 4384 births in a year The mean number of births per day is, Let X…

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

### Probability Distributions: Parking Tickets Issuance

#### Problem 5:
Tina is a traffic warden. The number of parking tickets she issues per day, from Monday to Saturday inclusive, may be modelled by a Poisson distribution with a mean of 11.5. By using suitable approximating distributions, find:

(i) The probability that on a particular Tuesday she issues at least 15 parking tickets.

(ii) The probability that during any week (excluding Sunday) she issues at least 50 parking tickets.

(iii) The probability that during four consecutive weeks she issues:

(a) At least 50 parking tickets each week.

(b) At least 200 parking tickets altogether.

**Note:** You must account for the difference in the two answers.

---

These problems require an understanding of the Poisson distribution and approximation techniques commonly used in probability theory and statistics.

1. **Poisson Distribution**: This is a probability distribution that models the number of events occurring within a fixed interval of time or space.

2. **Approximations**: For large sample sizes or specific conditions, different approximations (such as normal or binomial approximations) might be employed to simplify the calculations.

The steps involved in solving these problems typically include determining the mean and variance of the distribution, identifying the appropriate approximation, and then using statistical techniques or tools to find the required probabilities.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Given data,

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 5 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

A large manufacturing plant keeps track of the number of accidents per month. Suppose that accident counts over time follow a Poisson distribution with a mean of 7 per month. What is the probability of exactly 6 accidents in a month? 0.0912 0.1277 0.1304 0.1490 0.1014 m ♫ MA Ⓒ MacBook Pro W P f
The number of work-related injuries per month in a manufacturing plant is known to follow a Poisson distribution, with a mean of 4.0 work-related injuries a month. What is the probability that in a given month, no work-related injuries occur? That at least one work-related injury occurs?
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?
In a recent year, a hospital had 4142 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 13 births. Does it appear likely that on any given day, there will be exactly 13 births?
The number of earthquakes per day in the world has a Poisson distribution with parameter ?= 55. Suppose that the random variable X is the number of earthquakes occurring in one day in the world. Let the random variable Y be the total number earthquakes occurring in the world in 3 days. The Poisson distribution is very useful in analyzing phenomena which occur randomly in space or time.a. For our model, what is expected value of X? b. What is the probability that X = 55? c. What is the probability that X > 55? d. What is the probability that X >60? e. What is the smallest value C so that there is at least a 0.9 probability of no more than C earthquakes in a day? f. Y also has a Poisson distribution. What is the parameter ?y for Y? g. What is the standard deviation of X? h. What is the probability Y =164? i. What is the probability that Y < 164? j. What is the probability that X>60 given that X>55?
Power failures occur at an electric plant on average 3 times per year. If we can assume this follows a Poisson distribution, answer the following questions. a. What is the probability that there are 4 power failures in 2021? b. What is the probability that there are no more than 2 power failures in a given year? c. How likely is it that there are at least 3 power failures next year?
Hits to a high-volume website are assumed to follow a Poisson distribution with a mean of 1200 per day. What is the probability that the number of hits to the website tomorrow will be between 1190 and 1220 (inclusive)?