Homework 4: Probability and z scores

14. Use the data to answer the following questions
14. Show all work (*round 2 decimals places)

• What is the mean & SD for the distribution of scores?
• What is the corresponding z score for each raw score?
• What is the probability of getting a raw score greater than 4?
• What is the probability of getting a raw score less than 2?
• What is the probability of a raw score between 4 & 6?
• What is the probability of a raw score between 3 & 6?

Find the reduced row echelon form of the following matrices. Interpret your result by giving the solutions of the systems whose augmented matrix is the one given.

[ 0 0 3 -1 5

1 0 0 4 2

4 1 3 0 -8

1 2 7 9 0 ]

Researchers were interested in the relationship between mental health and living with a pet. Students were surveyed and grouped by pet type as either “Cats”, “Dogs”, or “No Pets”, and completed a scale on depressive symptoms on a scale of 1-7, where 7 indicates high levels of depressive symptoms. Using the data in the frequency table below, please conduct a one-way ANOVA to determine if there are any significant differences between these groups. Use α = .05, report η², and if the ANOVA is significant conduct a post-hoc test using Scheffe procedure. Finally, please report your answer in words and show all work and calculations step by step (don't forget to include the ANOVA table).

You are strongly encouraged to do your work in tables to help structure your work and keep it easily visible in your images. All work must be done by hand.

Java please. No "hard coding" please. Need to ask for the file and load the sample file information into the class.

There is a complete theory about how queues work. In this problem create a limited model to study the order in which a bunch of customers will be attended by their cashiers on a supermarket. The conditions for the experiment are:

• Each cashier spends the same amount of time with each customer (this is just an exercise, not real life).

• There will be a defined number of queues but never less than 2 and never more than 5.

• There is a variable number of customers, never less than 1 and never more than 20 and they are identified by a letter (A, B, C, …)

• The customers are distributed randomly among the different queues. • If two customers are served at the same time, we would consider that they will be ordered following the queue number they are at (first will be customer in queue 1, second customer in queue 2)

Write a program to give the order in which the customers are attended, for example:

• There are 4 queues:

• Cashier number 1 spends 3 minutes on each customer

• Cashier number 2 spends 2 minutes on each customer

• Cashier number 3 spends 4 minutes on each customer

• Cashier number 4 spends 1 minutes on each customer

• Customers are distributed as follows:

• Queue 1 (Cashier 1): Customer A, customer E, customer I

• Queue 2 (Cashier 2): B, F, J, N

• Queue 3 (Cashier 3): C, G, L

• Queue 4 (Cashier 4): D, H, M, O, P, Q

With this input the customers will have been served in the following order and timing:

D (after 1 minute)

B (after 2 minutes on queue 2)

H (after 2 minutes on queue 4)

A (after 3 minutes on queue 1)

M (after 3 minutes on queue 4)

F (after 4 minutes on queue 2)

C (after 4 minutes on queue 3)

O (after 4 minutes on queue 4)

P (after 5 minutes)

E (after 6 minutes on queue 1)

J (after 6 minutes on queue 2)

Q (after 6 minutes on queue 4)

N (after 8 minutes on queue 2)

G (after 8 minutes on queue 3)

I (after 9 minutes)

L (after 12 minutes)

The input from a data file will have the number of queues on the first line, followed by the information for each queue, first the time spent by the cashier on a customer, the number of customers on a queue and then the order of the customers separated by a space.

Output to the screen the list of served customers ordered by the time spent in the queue separated by spaces.

Must use a queue data structure.

Refer to the sample output below.

Sample File: the following information is on the queues.txt file

4

3 3 A E I

2 4 B F J N

4 3 C G L

1 6 D H M O P Q

Sample Run:

Enter file name: queues.txt

The list ordered by time spent: D B H A M F C O P E J Q N G I L

The JM Partnership was formed to acquire land and subdivide it as residential housing lots. On March 1, 2019, Jessica contributed land valued at $600,000 to the partnership, in exchange for a 50% interest in JM. She had purchased the land in 2011 for $420,000 and held it for investment purposes (capital asset). The partnership holds the land as inventory.

On the same date, Matt contributed land valued at $600,000 that he had purchased in 2009 for $720,000. He also became a 50% owner. Matt is a real estate developer, but this land was held personally for investment purposes. The partnership holds this land as inventory.

In 2020, the partnership sells the land contributed by Jessica for $620,000. In 2021, the partnership sells the real estate contributed by Matt for $580,000.

a. What is each partner's initial basis in his or her partnership interest?

Jessica's initial basis is $420000. Matt's initial basis is $720000.

b. What is the amount of gain or loss recognized on the sale of the land contributed by Jessica? What is the character of this gain or loss?

The amount of the gain  recognized on the sale of the land contributed by Jessica is $200000, and the type is ordinary income .

c. What is the amount of gain or loss recognized on the sale of the land contributed by Matt? What is the character of this gain or loss?

The amount of the loss  recognized on the sale of the land contributed by Matt is $____________, and the type is part capital loss and part ordinary loss .

d. How would your answer in (c) change if the property was sold in 2026?

The amount of the loss  recognized on the sale of the land contributed by Matt is $_________________, and the type is ordinary loss .

The Cronch Café, located at the Gulf of Mexico, has an increase in business during the summer vacation season. The owner hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered this sample information. 1) Develop a multiple regression equation with the amount of tips as the dependent variable and the amount of the bill and the amount of diners as independent variables. Write out the regression equation. How much does another diner add to the amount of the tips? 2) Conduct a global test of hypothesis to determine if at least one of the independent variables is significant What is your conclusion? 3) Conduct an individual test on each of the variables. Should one or the other be deleted? Plot the residuals against the fitted values. Is it reasonable to conclude they are random?

The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.

1. c-1. Conduct an individual test on each of the variables. What is the decision rule at the 0.05 level of significance? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Determine whether the polynomial is reducible or irreducible in the given polynomial ring. Justify your answers.

(c) x^4 + 1 in Z5[x]

(e) 2x^3 − 5x^2 + 6x − 2 in Z[x]

(f) x^4 + 4x^3 + 6x^2 + 2x + 1 in Z[x]. Hint: Substitute x − 1 for x.