The normal distribution or bell-shaped curve from statistics provides an example of a continuous probability distribution curve. While calculating the probability of the occurrence of an event, we find that the area under the curve between the desired range of profitability values is 0.438. What does this mean?

A. The probability of the occurrence of the event is 56.2 percent.

B. The probability of the occurrence of the event is 0.438 percent.

C. The probability of the occurrence of the event is 43.8 percent.

D. The probability of the occurrence can now be calculated by multiplying this number with the standard deviation.

E. The probability of the occurrence of the event is 0.562 percent.

Can I have this answer in a screenshot of the python software?

In the game of Lucky Sevens, the player rolls a pair of dice. If the dots add up to 7, the player wins $4; otherwise, the player loses $1. Suppose that, to entice the gullible, a casino tells players that there are many ways to win: (1, 6), (2, 5), and soon. A little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people's eyes glaze over at the first mention of mathematics “wins $4”.

      Your challenge is to write a program that demonstrates the futility of playing the game. Your Python program should take as input the amount of money that the player wants to put into the pot, and play the game until the pot is empty.

            The program should have at least TWO functions (Input validation and Sum of the dots of user’s two dice). Like the program 1, your code should be user-friendly and able to handle all possible user input. The game should be able to allow a user to ply as many times as she/he wants.

            The program should print a table as following:

      Number of rolls            Win or Loss                 Current value of the pot

                  1                                 Put                                    $10

                  2                                 Win                                  $14

                  3                                 Loss                                  $11

                  4

                  ##                              Loss                                  $0

        You lost your money after ## rolls of play.

        The maximum amount of money in the pot during the playing is $##.

        Do you want to play again?

      At that point the player’s pot is empty (the Current value of the pot is zero), the program should display the number of rolls it took to break the player, as well as maximum amount of money in the pot during the playing.

        Again, add good comments to your program.

        Test your program with $5, $10 and $20.

Let’s see whether quadratic voting can avoid the paradox of voting that arose in Table 5.3 when using 1p1v in a series of paired-choice majority votes. To reexamine this situation using quadratic voting, the table below presents the maximum willingness to pay of Garcia, Johnson, and Lee for each of the three public goods. Notice that each person’s numbers for willingness to pay match her or his ordering of preferences (1st choice, 2nd choice, 3rd choice) presented in Table 5.3. Thus, Garcia is willing to spend more on her first choice of national defense ($400) than on her second choice of a road ($100) or her third choice of a weather warning system ($0).

a. Assume that voting will be done using a quadratic voting system and that Garcia, Johnson, and Lee are each given $500 that can only be spent on purchasing votes (i.e., any unspent money has to be returned). How many votes will Garcia purchase to support national defense? How many for the road? Place those values into the appropriate blanks in the table below and then do the same for the blanks for Johnson and Lee. Assume there are no additional costs beyond the cost of purchasing votes and that votes must be purchased in whole numbers.

Instructions: Enter your answers as a whole number.

b. Across all three voters, how many votes are there in favor of national defense? The road? The weather warning system?

     Votes for national defense:

     Votes for road:

     Votes for weather warning system:

c. If a paired-choice vote is taken of national defense versus the road, which one wins?

      (Click to select)  National defense  Road  Indeterminate

d. If a paired-choice vote is taken of the road versus the weather warning system, which one wins?

      (Click to select)  Indeterminate  Weather warning system  Road

e. If a paired-choice vote is taken of national defense versus the weather warning system, which one wins?

      (Click to select)  Indeterminate  Weather warning system  National defense

Hummingbirds randomly fly through my back yard at a rate of 5 hummingbirds per hour. Let X = the number of hummingbirds who fly through my backyard during a randomly selected one-hour period. X may be modeled as a Poisson random variable with parameter λ = 5. Let Y equal the total number of hummingbirds who fly through my backyard during a randomly selected two-hour period.

a. For our model, what is expected value of X?
b. What is the probability that X = 4?
c. What is the probability that X < 5?
d. What is the probability that X > 9
e. What is the probability that X = 0
f. Y also has a Poisson distribution. What is the parameter λ for Y?
g. What is variance of Y?
h. What is the standard deviation of Y?
i. What is the probability that Y = 8
j. What is the probability that Y > 8?

Julien has three boxes of socks. In the first he has 3 white and 2 blue socks, in the second he has 4 red and 3 white, while in the third box he has 3 red and 4 blue.
Julien chooses a box uniformly and fishes two socks out of it.

(a) What is the probability of Julien getting at least one red stocking?
(b) What is the probability that Julien will receive a matching pair of socks if he chooses box number one?
(c) What is the probability that Julien will receive a matching pair of socks?
(d) Given that Julien received a matching pair of socks, what is the probability that he chose box number 1?

At one point during the COVID-19 crisis, the probability that an person who tested positive for the illness would infect another person they came into contact with was 75% . Suppose on that day, the infected person came into contact with 15 other people.

For each part below, show the formula set-up and round your final answers to four decimal places.

a) The probability the ill person infected exactly 10 people out of the 15.

b) the probability the ill person infected at most 2 of the 15 people.

c) the probability the ill person infected at least 3 people out of the 15.

d) what are the expected number of people the ill person will infect? Round to the nearest whole number.

question 1. In STAT4800-W02, there are two term tests and, it is believed that the term test 2 is harder than
the term test 1. You believe the probability you pass the term test 1 is 70%. If you pass the term
test 1, the probability you also pass the term test 2 will be 80%, and if you fail the term test 1,
the probability you pass the term test 2 will be 20%. Let ? be the number of term tests you pass.
a) Find the probability model for ?.
b) Find and interpret the expected number of tests you pass. What is your recommendation to
your friend, about this instructor, who is planning to take the STAT4800 in next semester?
(1.5 marks)

1. From past experience it is known that 90% of one-year old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 50 one-year olds is given this voice recognition test.
   1. Find the probability that exactly 3 children do not recognize their mother’s voice. (2 points)
2. 2. Find the probability that 3 or fewer children do not recognize their mother’s voice. (2 points)
3. 3. What is the probability that at least 47 children recognize their mother’s voice?(2 points)
4. 4. Find the probability that exactly 90% of the 50 children do recognize their mother’s voice. (2 points)
5. 5. What is the probability that exactly 49 of the 50 children recognize their mother’s voice? (2 points)
6. 6. Find the probability all 50 children recognize their mother’s voice. (2 points)
7. 7. Let the random variable x denote the number of children who recognize their mother’s voice. Find the mean of x. (2 points)
8. 8. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the mean of x. (2 points)
   8. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the variance of x. (2 points)

1) Is the following study design an anecdote, experiment, or observational study?

You'd like to investigate if what color shirt fans wear to a game help the Le Moyne Women's Soccer team score goals? You attend every home game. You write down how many fans attended the game, what color shirt they wore, and how many goals the soccer team scored.

2) Among the 268 words in the Gettysburg Address, 99 contain at least 5 letters. Is 99/268 = .369 a statistic, a parameter, or neither?

3) If you calculate the average number of hours that students in your class slept last night, describe (in words) the corresponding parameter of interest.

The parameter of interest is the average number of hours that  students slept last night.

4) If the mean of a distribution is 75 and the standard deviation is 9, how many standard deviations above the mean is 120?

5) A 1999 Gallup survey of a random sample of 1005 adult Americans found that 69% planned to give out Halloween treats from the door of their home. Does this finding necessarily prove that 69% of all adult Americans planned to give out treats? (yes/no)

6) I have a 3/5 = .60 probability of winning a game of solitaire.

How many games do I have to play before I can use the CLT to reasonably approximate the sampling distribution of the sample proportion of wins?

7) Suppose author A and Author B are doing studies on the same variable. Author A collects a sample of size 50 and Author B collects a sample of size 200. It turns out they both happen to get identical sample statistics. They then both construct 95% confidence intervals. Who has the smaller confidence interval? (A/B)

8) As sample size increases, the standard deviation (increases/decreases/stays the same)