代写Group Project 3, Flavour C代做Java语言

Group Project 3, Flavour C

In this project, you will investigate a probabilistic model of group behaviour. The model will help you plan a policy to implement.

Your group submission must be typed, and marks will be awarded for communication (see Canvas assign ment).

Learning Objectives

• Understand how to work with probability density functions (PDFs).

• Practice working with mathematical models and interpreting prose in context.

• Communicate mathematical content clearly and effectively in prose.

Contributors

On the first page of your submission, list the student numbers and full names (with the last name in bold) of all team members.

After submitting this assignment, you will provide feedback on your teammates’ contributions using iPeer. If there is zero contact with a group member, please mark NP (for ‘non-participating’) beside their name in this list, and award a 0 on iPeer.

Reflection

1. Now that you have completed all of the group projects for this course, reflect on the value of collaborative work in your learning of calculus.

(a) Briefly describe how the collaboration with your group worked. For example, was the collaboration centred around the discussion of solution strategies, or was it focused more on the logistics of compiling a set of solutions efficiently? What prompted the collaboration?

(b) (Each group member should answer this question individually.) Did you find working in groups on these projects useful for your own learning of calculus? Why or why not?

(c) Have there been other instances in this course (in class or out of class) when you worked with peers (either in your group or with other Math 101 students) productively and improved your learning of calculus? What made the collaboration productive?

Assignment questions

Note: for this assignment, you may use a scientific calculator to simplify your final expressions (for example, to turn expressions such as e/1 into decimals).

An airline has studied the times that people show up for their flight, relative to the time they are told to show up.

Let X be a random variable that gives the number of minutes after the instructed time that a person chosen at random shows up. (So for example, if the chosen person was told to show up at 11, and they show up at 10:30, then X = −30.) We’ll assume at first that the probability density function (PDF) f(x) is the same for everyone. Specifically,

Let’s say that a person must be at the gate by noon in order to get on the plane. Anyone arriving after noon misses the plane; anyone arriving before noon makes it on. In this assignment, we’ll investigate the time that the airlines should tell their customers to arrive at the gate.

2. (3 points) Suppose the airline tells passengers to be at the gate at 11:00. What is the probability that a person will make it to the gate before noon? Extrapolating from this, what percentage of people do you expect to actually make it on the flight?

3. (5 points) What time, rounded to the nearest minute, should an airline tell their customers to come if they want 90% of them to make the flight? What about 95%?

4. (4 points) We often talk about the group of outcomes that are within one standard deviation from the expected value of a variable. If the airline wants people who come at most E(X) + σ(X) minutes late to be able to board, what time should they tell people to come?

5. After further study, the airline has begun to quantify the different habits of different groups of passengers. They find the following:

• For 50% of the population of customers, the PDF of X is f(x).

• For 30% of the population of customers, the PDF of X is g(x).

• For 15% of the population of customers, the PDF of X is h(x).

• For 5% of the population of customers, the PDF of X is k(x).

The four PDFs are graphed below.

(a) (2 points) Match the PDFs to the following descriptions of customers:

A. Generally a little early to the gate.

B. Generally a little late to the gate.

C. Generally very early to the gate.

D. Generally very late to the gate.

Match one PDF to each description. Use qualitative descriptions of the graphed PDFs to justify your answers.

(b) (3 points) Two of the PDFs have relatively high variances, and two of them have relatively low variances.

i. Which PDFs have high variances, and which have low variances? How can you tell?

ii. Give a reason why a plane full of customers described by a PDF with low variance f(x) might be easier to accommodate than a plane full of customers described by g(x).

iii. Give a reason why a plane full of customers described by g(x) might be easier to accommodate than a plane full of customers described by f(x).