1. For the andorian species, if the probability that a couple produces a girl is 0.97193, and if the couple has 8 children, what is the probability they will have:
5 boys and 3 girls (in any order)?

2. For the Vulcan species, if the probability that a couple produces a girl is 0.23477, and if the couple has 5 children, what is the probability they will have:
3 boys and 2 girls (in any order)?

Q 4
A computer program translates texts between different languages. Experience shows that the probability of a word being incorrectly translated is 0.002.
We enter a text with 5000 words.
What is the probability that no word is translated incorrectly? (Tips, Po)
What is the probability that at most 2 words will be translated incorrectly?
What is the probability that 3 or more words are translated incorrectly?

Each player throws both dice once per turn. The player only scores when the player throws doubles. Double-6 scores 25 points. A double-3 cancels out a player’s score and puts the score back to zero. Any double other than a 3 or 6 scores 5 points. Scores are recorded and the first player to obtain a total score of fifty points wins the game.

Write a MATLAB program to simulate the FIFTY dice game that can:

1. Play the FIFTY dice game automatically for one player using two dice.

2. Add your name, purpose, and copyright your program.

3. Clear command window and clear all variables.

4. Randomize the pseudorandom number generator with the MATLAB built-in rng function and provide ‘shuffle’ as the function input.

5. Create a variable that will keep the game score. Set the value of this variable to 0.

6. Create another variable that will count the round number. Set the value of this variable to 1.

7. Welcome the player and briefly explain how to play the game when the program starts.

8. Print the current round number in the command window.

9. Print the current game score in the command window.

10. Generate two random integers between 1 and 6 to represent the face values of two dice.

11. Print the two dice values in the command window.

12. If the value of the 1 st die and the 2nd die are not equivalent with each other: a. No action required. We can optionally display a message that no point will be added to the game score.

13. Else a. If the value of the first die is equivalent with 3: i. Display a message about rolling a double 3 causes the game score to set back to 0. ii. Set the game score to 0. b. Elseif the value of the first die is equivalent with 6: i. Display a message about rolling a double 6 adds 25 points to the game score. ii. Set the game score to game score plus 25. c. Else: i. Print a message about rolling the double dice adds 5 points to the game score. ii. Set the game score to game score plus 5. d. End.

14. End.

15. Increment the round number by 1.

16. The game should keep playing while the player’s game score is less than 50 points. Insert a while loop to wrap around the code generated from step 8 through step 15. Make the existing code generated from steps 8 through 15 the code block of this new while loop.

17. Congratulate the player and show the player’s final game score in the command window.

Identify the factors, levels, and total number of groups for each of the following research examples. State both the number of levels for each factor and describe each in words.

1. A consultant is hired by a business concerned about their low sales the previous quarter. She notices that this business has a large number of part-time employees and that not all employees went through the orientation training. She believes that these factors may be contributing to the low productivity. To test this, she measures productivity (as number of units sold) among part-time and full-time employees who did or did not receive orientation training upon to being hired.

Dependent variable:           _______________________________________

Factor A:                            _______________________________________

Levels of Factor A :           _______________________________________

Factor B:                             _______________________________________

Levels of Factor B:             _______________________________________

Number of groups:            __________

2. A psychologist believes that perception is influenced by a motivational bias (a bias to satisfy an individuals personal needs, such as their desire for control or power). The psychologist believes this bias is especially present in the context of sports. To test this, the psychologist had a group of sports fans watch a recorded football game where many penalties were called on each team. The participants were fans for either the home team, the away team, or were not a fan of either team. The number of penalties that each type of fan (neutral fan, home fan, away fan) disagreed with during the game for each team (home team, and away team) was recorded. It was expected that if fans showed a motivational bias, then they would disagree more often with penalties called against the team they were rooting for; whereas neutral fans should show the least disagreement overall.

Dependent variable:           _______________________________________

Factor A:                            _______________________________________

Levels of Factor A:                        _______________________________________

Factor B:                             _______________________________________

Levels of Factor B:             _______________________________________

Number of groups:             __________

3. A professor suggests that her college students will attend class more if quizzes were given in every class. To demonstrate the need for this change, the professor records the attendance of students (as the number of absences) in morning versus evening classes in which quizzes are given every class or just once a week. She hypothesized that attendance would be highest in the classes with quizzes in each class.

Dependent variable:           _______________________________________

Factor A:                            _______________________________________

Levels of Factor A:                        _______________________________________

Factor B:                             _______________________________________

Levels of Factor B:             _______________________________________

Number of groups:             __________

4. A researcher notes that male-female pairs of fraternal twins share a similar environment in a mothers’ womb. This exposes the female twin to higher levels of the hormone testosterone during prenatal development. This hormone is thought to be responsible for masculinizing the brain (it leads to male-typical behaviors). Likewise, the male twin is exposed to higher levels of the hormone estrogen. This hormone is thought to be responsible for feminizing the brain (it leads to female-typical behaviors). To test whether exposure to testosterone and estrogen may influence male and female typical behavior, the researcher selected a sample of female-male fraternal twins and compared them to identical twins of each gender (male, female). She measured tendencies toward aggression using an aggression assessment where higher scores indicated greater aggression (a male-typical trait). It was hypothesized that if hormone exposure influenced behavior, then aggression scores will vary among the groups.

Dependent variable:           _______________________________________

Factor A:                            _______________________________________

Levels of Factor A:                        _______________________________________

Factor B:                             _______________________________________

Levels of Factor B:             _______________________________________

Number of groups:             __________

Think of scenario in which probability can be used in everyday life ( weather forecasts, car insurance). Describe the how statistics of the probability could be used and what some outcomes of the probability . Site source.

The following frequency distribution shows the ages of India’s 53 richest individuals. One of these individuals is selected at random.

a. What is the probability that the individual is between 50 and 60 years of age? (Round your answer to 3 decimal places.)

Probability:_______

b. What is the probability that the individual is younger than 50 years of age? (Round your answer to 3 decimal places.)

Probability:_______

c. What is the probability that the individual is at least 60 years of age? (Round your answer to 3 decimal places.)

Probability:_______

6. An expert sharpshooter misses a target 10 percent of the time.
(a) What is the probability that she misses the target for the first time in her second shot? (b) What is the probability that she misses the target for the first time in her xth shot? (c) What is the probability that the first miss comes after the 3rd shot? (d) How many shots does she expect to fire to suffer the first miss? (e) What is the probability that she will suffer 2 misses from 10 shots? (f) What is the probability that she will suffer at least 1 miss from the 10 shots? (g) What is the probability that she misses the target for the second time in her 10th shot?

3. For the Romulan species, if the probability that a couple produces a girl is 0.2563, and if the couple has 7 children, what is the probability they will have: 2 boy(s) and 5 girl(s) (in any order)?

4. For the Romulan species, if the probability that a couple produces a girl is 0.73991, and if the couple has 5 children, what is the probability they will have: 4 boy(s) and 1 girl(s) (in any order)?

5. For the Andorian species, if the probability that a couple produces a girl is 0.92162, and if the couple has 7 children, what is the probability they will have: 4 boy(s) and 3 girl(s) (in any order)?

Need help with #3, 4, and 5. please showed works and neat writing. Thank you

1

x is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for:     n = 7,    x = 3,    p = 0.9
P(x) =   

(b) Calculate the probability of x for:     n = 5,    x = 4,    p = 0.25
P(x) =  

(c) Calculate the probability of x for:     n = 8,    x = 2,    p = 0.6
P(x) =   

(d) Calculate the probability of x for:     n = 6,    x = 5,    p = 0.45
P(x) =   

(e) Calculate the probability of x for:     n = 10,    x = 8,    p = 0.8
P(x) =   

(f) Calculate the probability of x for:     n = 8,    x = 7,    p = 0.45
P(x) =