11. Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $12,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniformly distributed between $12,000 and $17,000.

a. Suppose you bid $13,000. What is the probability that your bid will be accepted?

b. Suppose you bid $16,000. What is the probability that your bid will be accepted?

c. What amount should you bid to maximize the probability that you get the property?

d. Suppose you know someone who is willing to pay you $18,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?

The mean cost of domestic airfares in the United States rose to an all-time high of $375 per ticket. Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $115. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $540 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $255 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $310 and $500 (to 4 decimals)?

d. What is the cost for the 5% highest domestic airfares? (rounded to nearest dollar) (X) $ or (more/less)

The mean cost of domestic airfares in the United States rose to an all-time high of $400 per ticket. Airfares were based on the total ticket value, which consisted of the price charges by the airlines plus any additional taxes and fees. Assume domestic airfares are normally distributed with a standard deviation of $120. Use Table 1 in Appendix B.

a. What is the probability that a domestic airfare is $555 or more (to 4 decimals)?

b. What is the probability that a domestic airfare is $250 or less (to 4 decimals)?

c. What if the probability that a domestic airfare is between $300 and $470 (to 4 decimals)?

d. What is the cost for the 4% highest domestic airfares? [(round to nearest dollar) (more or less)]

A sample of 16 Triple-A minor league baseball teams were selected for statistical analysis. The following data show the average attendance for the 16 teams selected. Also shown are the teams’ records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.  Additionally, each teams’ major league association was given. The data are contained in the file named AAA.

1. Graph and Summary statistics:  present a graph that summarizes the data along with a table of summary statistics for each variable in the data set.  An interpretation must accompany any graph, chart, or table that you use.
2. Methods:  
   1. Develop estimated regression equations, first using attendance as the dependent variable and then using number of wins as the independent variable. Discuss your findings.
   2. Develop an estimated regression equation with attendance as dependent variable and both league and wins as the independent variables.  Discuss your findings.
   3. What is the predicted attendance for an America league AAA team with 72 wins?

use c++
This question is about providing game logic for the game of craps we developed its shell in class. At the end of the game, you should ask the user if wants to play another game, if so, make it happen. Otherwise, quit

**Provide the working output of this game and the picture of the output. **

This is an implementation of the famous 'Game of Chance' called 'craps'.
It is a dice game. A player rolls 2 dice. Each die has six faces: 1, 2, 3, 4, 5, 6.
Based on the values on the dice, we play the game until a player wins or loses.
You add the values of the dice's face.
1) If the sum is 7 or 11 on the first roll, the player wins.
2) If the sum is 2, 3, or 12 on the first roll, the player loses ( or the 'house' wins)
3) If the sum is 4, 5, 6, 8, 9, or 10 on the first roll, then that sum becomes the player's 'point'.
4)To win, the player must continue rolling the dice until he/she 'make the point'.
5)If the player rolls a 7 he/she loses.

#include <cstdlib>
#include <ctime>
#include <iostream>
#include <random>

enum class Status { CONTINUE, WON, LOST};

unsigned int rollDiceAdvanced(); // same as above, but used advance c++ Random Number generation.

   // global variable to use in the advanced version of RNG (Random number Generator)
std::default_random_engine engine{ static_cast<unsigned int>(time(0)) };
std::uniform_int_distribution<unsigned int> randomInt{ 1, 6 };

int main()
{
   Status gameStatus; // can be CONTINUE, WON, or LOST
   unsigned int myPoint{ 0 };
  

   unsigned int sumOfDice = rollDiceAdvanced(); // first roll of dice.

   // bellow the game logic: Provide the game logic

   return 0;
}
// this is distribution based random number generation in c++
unsigned int rollDiceAdvanced()
{
   unsigned int firstRoll{ randomInt(engine) };
   unsigned int secondRoll{ randomInt(engine) };
   unsigned int sum{ firstRoll + secondRoll };
   std::cout << "rollDiceAdvance: " << sum << std::endl;
   return sum;
}

Assume that a procedure yields a binomial distribution with 4 trials and a probability of success of 0.60 Use a binomial probability table to find the probability that the number of successes is exactly 4.

The probability that the number of successes is exactly 4 is nothing.

One die is rolled and one marble – yellow, blue, purple, or red is selected at random.

-Determine the number of possible arrangements.

-Determine the probability of obtaining the number 2 and the blue marble.

-Determine the probability of obtaining the number 3 or the red marble.

-Determine the probability of obtaining an odd number or the purple marble.

Part 1.

When a probability experiment only has two possible outcomes and you know the probability of one outcome, you can find the probability of the other outcome by computing (the complementary probability, using the addition rule, using the multiplication rule)

To find the probability of two (mutually exclusive, independent) events both occurring, you may simply multiply their individual probabilities.

When two scenarios are (mutually exclusive, independent) , we can simply add their probabilities together to find the probability that one scenario or the other scenario occurs.

Part 2.

When using the choose function, the top number n represents (number of successes, number of trials, probability) and the bottom number k represents (number of trials, probability, number of successes )

Part 3.

Suppose you flip a coin 6 times. For each of the 6 trials there are 2 possible outcomes, heads or tails. Heads and tails each have a probability of 0.5 per trial. Consider "heads" to be a success. What is the probability that you only have 2 successes in 6 trials? Round your answer to four digits after the decimal point.