Suppose that the average number of Facebook friends users have is normally distributed with a mean of 119 and a standard deviation of about 41. Assume forty-five individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 45, find the probability that the average number of friends is more than 114.
3. Find the third quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? NoYes

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 117 and a standard deviation of about 58. Assume forty-two individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 42, find the probability that the average number of friends is less than 104.
3. Find the first quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? NoYes

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 131 and a standard deviation of about 49. Assume seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 7, find the probability that the average number of friends is less than 150.
3. Find the first quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? NoYes

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 121 and a standard deviation of about 40. Assume forty-five individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

What is the distribution of x? x ~ N(___,____)

For the group of 45, find the probability that the average number of friends is less than 115. _____

Find the first quartile for the average number of Facebook friends. ____

For part b), is the assumption that the distribution is normal necessary? Yes or No

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 117 and a standard deviation of about 45. Assume forty-seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) For the group of 47, find the probability that the average number of friends is more than 121. Find the third quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? NoYes

CCA has stated in 2017 that 84.3 % of its students are first generation college students. Suppose you sample 15 CCA students and ask if they are first generation college students or not, counting the number of first generation students. a. Create a binomial probability distribution (table) for this situation. (Report answers accurate to 4 decimal places.)

BINOMIAL PROBABILITY TABLE:

k P(X = k)

0 8.6795E-13 Correct

1 6.99059E-11 Correct

2 2.627 Incorrect

3 6.1135 Incorrect

4 9.8478E-07 Correct

5 1.16329E-05 Correct

6 0.000104104 Correct

7 0.000718685 Correct

8 0.003858928 Correct

9 0.016115737 Correct

10 0.051919361 Correct

11 0.126716912 Correct

12 0.22679906 Correct

13 0.28102637 Correct

14 0.215564359 Correct

15 0.077163802 Correct

a. What is the probability that 11 students or less are first generation? 0.927270503

b. What is the probability that at least 7 students are first generation ? 0.000835471

c. What is the probability that 4 students will be first generation?

d. What is the probability that between 7-14 students are first generation (including 7 and 14)? 0.922719412 Correct

e. What is the probability that 7 students are NOT first generation?

problem 3-1

You are going to build a C++ program which runs a single game of Rock, Paper, Scissors. Two players (a human player and a computer player) will compete and individually choose Rock, Paper, or Scissors. They will then simultaneously declare their choices and the winner is determined by comparing the players’ choices. Rock beats Scissors. Scissors beats Paper. Paper beats Rock.

The learning objectives of this task is to help develop your understanding of abstract classes, inheritance, and polymorphism.

Your task is to produce a set of classes that will allow a human player to type instructions from the keyboard and interact with a computer player.

Your submission needs to contain the following files, along with their header files:

• main-3-1.cpp
• Player.cpp
• Person.cpp
• Computer.cpp

Part 1: Abstract Classes

Define and implement an abstract class named Player that has the following behaviours:

void move();
string getMoves();
char getMove(); //returns the most recent move made
bool win(Player * opponent); //compares players’ moves to see who wins

Declare the move() and getMoves() functions as pure virtual and set proper access modifiers for the attributes and methods.

If no one wins, the game should output “draw! go again”, and the game continues until a winner is determined.

Part 2: Polymorphism

Computer Class:

Define and implement a class named Computer that inherits from Player. By default, Computer will use Rock for every turn. If it is constructed with another value (Paper or Scissors), it will instead make that move every turn.

The Computer class has the following constructor and behaviours:

Computer(string letter); //set what move the computer will
//make (rock, paper, or scissors)
//if the input is not r, R, p, P, s, S or
//a string starting with one of these letters,
//set the move to the default ‘r’

string getMoves(); //returns all moves stored in a string

void move(); //increments number of moves made

To explain, if the computer was constructed with Computer(‘s’), and it made 3 moves, getMoves() should return:

sss
For advice about testing, please use the debugging manual (Links to an external site.).

Person Class:

Define and implement a class named Person that inherits from Player. The Person can choose Rock, Paper, or Scissors based on the user’s input.

The Player class has the following behaviours:

void move(); //allow user to type in a single character to
//represent their move. If a move is impossible,
//“Move unavailable” is outputted and the user is
//asked to input a character again.
//Otherwise, their input is stored

string getMoves();   //returns all moves stored in a string

Write a main function that uses Computer and Person to play Rock, Paper, Scissors. The Computer can be made with either constructors, but should set the default move to ‘r’. The player should be asked to input a move which is then compared against the computer’s move to determine who wins.

All the Player’s previous moves should be outputted, followed by all the Computer’s moves outputted on a new line.

Example Test Cases

Just two quick questions!

Read Questions Please. Its different from the others thats been posted!

Information

Six months before its annual convention, the American Medical Association (AMA) must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $100 per room. The AMA believes the number of doctors attending the convention will be has a triangular distribution with minimum value 2000, maximum value 7000, and most likely value 5000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $ 160 per room. Assume that there are 8000 rooms available.

[Round your answers to the nearest integer. Also just enter the number. For example, if your answer is $123,456, then enter 123456 without $ and comma.]

Information

Build a simulation model assuming the number of doctors attending the convention follows the following probability distribution.

Run the simulation model 50,000 times.

Question 7 (3 points)

If they reserve 3000 rooms now, the expected total cost is

Your Answer:

Question 8 (3 points)

If they reserve 6000 rooms now, the expected total cost is

Your Answer:

In all parts of this problem, assume that we are using fair, regular dice (six-sided with values 1, 2, 3, 4, 5, 6 appearing equally likely). Furthermore, assume that all dice rolls are mutually independent events.

(a) [4 pts] You roll two dice and look at the sum of the faces that come up. What is the expected value of this sum? Express your answer as a real number.

(b) [7 pts] Assuming that the two dice are independent, calculate the variance of their sum. Express your answer as a real number.

(c) [7 pts] You repeatedly roll two fair dice and look at the sum. What is the probability that you will roll a sum of 4 before you roll a sum of 7? Express your answer as a real number.

(d) [7 pts] What is the expected number of rolls until you get a sum of 4 or a sum of 7? (For example, if you get 7 on the first roll, the number of rolls is 1.) Express your answer as a real number.

(e) [7 pts] You roll 10 dice. Using the Chernoff Bound, give an upper bound for the probability that 8 or more of them rolled a 1 or a 2? You don’t need to calculate the value with a calculator (since you do not have one), but please write it in simplest terms.

I only need the solution for 5.130

The Christmas Bird Count (CBC) is an annual tradition in Lexington, Massachusetts. A group of volunteers counts the number of birds of different species over a 1-day period. Each year, there are approximately 30–35 hours of observation time split among multiple volunteers. The following counts were obtained for the Northern Cardinal (or cardinal, in brief) for the period 2005–2011.

Year Number

2005 76

2006 47

2007 63

2008 53

2009 62

2010 69

2011 62

5.126 What is the mean number of cardinal birds per year observed from 2005 to 2011?

5.127 What is the standard deviation (sd) of the number of cardinal birds observed?

5.128 What is the probability of observing at least 60 cardinal birds in 2012? (Hint: Apply a continuity correction where appropriate.)

The observers wish to identify a normal range for the number of cardinal birds observed per year. The normal range will be defined as the interval (L, U), where L is the largest integer ≤ 15th percentile and U is the smallest integer ≥ 85th percentile.
5.129 If we make the same assumptions as in Problem 5.128, then what is L? What is U?

5.130 What is the probability that the number of cardinal birds will be ≥ U at least once on Christmas day during the 10-year period 2012–2021? (Hint: Make the same assumptions as in Problem 5.128.)