Given that in 4 flips of a fair coin there are at least two "heads", what is the probability that there are two "tails"? There are ten equally likely outcomes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You randomly select one value, call it the initial value. Then, you continue to randomly select values, call them follow-up selections, until you come up with the initial value. What is the fewest number of follow-up selections that insures that the probability is better than one-half that you will observe your initial value? (Note: this problem assumes values are selected "with replacement," which simply means that after each selection, there are still the same ten equally likely outcomes.)

Assume that a winning ticket is one which matches the 6 numbers drawn from 1 to 49.
(a) (1 mark) Suppose p is the probability of winning the grand prize. Write down the value for p for
Lotto 649.
(b) (1 mark) Write down the probability of winning (for the first time) on the nth draw (i.e. losing
on the first n − 1 draws).
(c) (1 mark) Determine the expected number of draws you must play (1 ticket each draw) before
winning for the first time.
(d) (1 mark) Show how the average time to win Lotto 649 when playing 1 ticket per weekly 649 draw
turns into the long wait given for the Homo sapiens example.

The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of nine syringes taken from the batch. Suppose the batch contains 1% defective syringes. (a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, , 8 and 9 defective syringes in a random sample of nine syringes. (b) Find μ. What is the expected number of defective syringes the inspector will find? (c) What is the probability that the batch will be accepted? (d) Find σ. Step 1 (a) Make a histogram showing the probabilities of r = 0, 1, 2, 3, , 8 and 9 defective syringes in a random sample of nine syringes. Recall that the binomial distribution with parameters n, p, and r gives the probability distribution of the number of r successes in a sequence of n trials, each of which yields success with probability p. Here we can let "success" be defined as "finding a defective syringe." The batch contains 1% defective syringes, so there is a 1% chance that any given syringe will be found to be defective. Therefore, p = 0.01 . A random sample of nine syringes are checked for quality, so n = 9

Step 2

We are interested in the probability of r defective syringes when r = 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Use this table to create a table of r values and the corresponding

P(r)

values when n = 9 and p = 0.01. (Round your answers to three decimal places.)

Please help find 1 ,2 and 4 in the map

PLEASE answer the question correctly and neatly so I'm able to see how you arrived at your answer. If you do not know how to round or answer the question correctly PLEASE do not answer.

You have $460,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $180,000. Consider the summary measures in the following table:

The correlation coefficient between your portfolio and the house is 0.33.

a. What is the expected return and the standard deviation for your portfolio comprising your old portfolio and the house? (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

b. Suppose you decide to sell the house and use the proceeds of $180,000 to buy risk-free T-bills that promise a 14% rate of return. Calculate the expected return and the standard deviation for the resulting portfolio. [Hint: Note that the correlation coefficient between any asset and the risk-free T-bills is zero.] (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

At a local community college, 43% of students who enter the college as freshmen go on to graduate. Seven freshmen are randomly selected.

a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

Complete parts (a) through (e), given Σx = 13, Σy = 148, Σx² = 65, Σy² = 5750, Σxy = 403, and

r ≈ −0.988.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

Complete parts (a) through (e), given Σx = 16, Σy = 152, Σx² = 78, Σy² = 6102, Σxy = 546, and

r ≈ −0.918.

(a) Draw a scatter diagram displaying the data.

b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

Complete parts (b) through (e), given Σx = 15, Σy = 152, Σx² = 77, Σy² = 6094, Σxy = 501, and r ≈ −0.849.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r²to three decimal places. Round your answers for the percentages to one decimal place.)

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
____%

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

Complete parts (a) through (e), given Σx = 16, Σy = 152, Σx² = 78, Σy² = 6130, Σxy = 540, and

r ≈ −0.966.

(a) Draw a scatter diagram displaying the data.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%

Tony Gaddis C++

Tic-Tac-Toe Write a program that allows two players (player X and player O) to play a game of tic-tac-toe. Use a two- dimensional char array with three rows and three columns as the game board. Each element of the array should be initialized with an asterisk (*). The players take turns making moves and the program keeps track of whose turn it is. Player X moves first. The program should run a loop that: Displays the contents of the board array (see prompts and output, below). Prompts and allows the player whose turn it is to select a location on the board for an X in the case of player X or an O in the case of player O. The program should ask the player to enter the row and column number. Valid row or column numbers are 1, 2, or 3. The loop terminates when a player has won, or a tie has occurred. If a player has won, the program should declare that player the winner and end. If a tie has occurred, the program should say so and end. Player X (O) wins when there are three Xs (three Os) in a row on the game board. The Xs (Os) can appear in a row, in a column, or diagonally across the board. A tie occurs when all of the locations on the board are full, but there is no winner. Input Validation: The program should check the validity of the row and column numbers entered by the players. To be valid, the row and column number must refer to an unoccupied position in the game board. When an invalid entry is made, the program simply redisplays its most recent prompt and attempts to reread the value.

Overbooking flights

Eagle Air is a small commuter airline.  Each of their planes holds 15 people. Past records indicate that only 80% of people with reservations (tickets) do show up. Therefore, Eagle Air decides to overbook every flight. Suppose Eagle Air decides that it will accept up to 18 reservations per flight (18 is the maximum number of reservations per flight).

Demand for Eagle Air flights is so strong that 18 reservations are booked for every flight. Everyone knows how popular Eagle Air flights are, and so no one ever shows up without a reservation.

This is the first of 6 questions in this set.

a. Calculate the probability that on any given flight, at least one passenger holding a reservation will not have a seat.  Four decimals

b. What is the probability that there will be one or more empty seats? Four decimals

c. What is the probability that the first person who is bumped from a flight will not get on either of the next two flights? Assume that the number of “no-shows” is independent across flights. Also assume that the first person who is bumped has priority when an empty seat comes up on a subsequent flight.  Four decimals

d. What is the expected number of people who show up for a flight? Reminder: Everyone makes a reservation ahead; no one shows up without a reservation; a maximum of 18 reservations is accepted; and every flight has 18 reservations because Eagle Air is so popular.  One decimal

e. Suppose that each flight costs $1000 to run, considering all costs. If tickets are priced at $75 each, what is Eagle Air’s expected profit per flight? Assume that when sixteen or more people show up for a flight, any overbooked passengers wait until a seat becomes available, so Eagle Air ultimately gets the revenue from everyone who shows up.  One decimal

f. What is the standard deviation of the number of people who show up for a flight? Two decimals