A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 475 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.5% and standard deviation σ = 1.1%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 475 stocks in the fund) has a distribution that is approximately normal? Explain.

Yes / No , x is a mean of a sample of n = 475 stocks. By the ______ theory of normality central limit theorem law of large numbers , the x distribution  ---Select--- is not is approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

No, the probability stayed the same.

Yes, probability increases as the standard deviation decreases.

Yes, probability increases as the standard deviation increases.

Yes, probability increases as the mean increases.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.5%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) = ____

Explain.

This is very likely if μ = 1.5%. One would suspect that the European stock market may be heating up.This is very unlikely if μ = 1.5%. One would not suspect that the European stock market may be heating up.    This is very likely if μ = 1.5%. One would not suspect that the European stock market may be heating up.This is very unlikely if μ = 1.5%. One would suspect that the European stock market may be heating up.

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 450 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.2% and standard deviation σ = 1.3%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 450 stocks in the fund) has a distribution that is approximately normal? Explain.

---Select--- Yes No , x is a mean of a sample of n = 450 stocks. By the  ---Select--- theory of normality law of large numbers central limit theorem , the x distribution  ---Select--- is is not approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

No, the probability stayed the same.Yes, probability increases as the mean increases.     Yes, probability increases as the standard deviation decreases.Yes, probability increases as the standard deviation increases.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.2%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =  

Explain.

This is very likely if μ = 1.2%. One would suspect that the European stock market may be heating up.This is very likely if μ = 1.2%. One would not suspect that the European stock market may be heating up.     This is very unlikely if μ = 1.2%. One would not suspect that the European stock market may be heating up.This is very unlikely if μ = 1.2%. One would suspect that the European stock market may be heating up.

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 200 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.3% and standard deviation σ = 1.1%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 200stocks in the fund) has a distribution that is approximately normal? Explain.

---Select--- Yes No , x is a mean of a sample of n = 200 stocks. By the  ---Select--- central limit theorem law of large numbers theory of normality , the x distribution  ---Select--- is is not approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

No, the probability stayed the same.Yes, probability increases as the mean increases.     Yes, probability increases as the standard deviation decreases.Yes, probability increases as the standard deviation increases.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.3%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =  

Explain.

This is very unlikely if μ = 1.3%. One would not suspect that the European stock market may be heating up.This is very likely if μ = 1.3%. One would not suspect that the European stock market may be heating up.     This is very likely if μ = 1.3%. One would suspect that the European stock market may be heating up.This is very unlikely if μ = 1.3%. One would suspect that the European stock market may be heating up.

QUESTION 1

a) It is now known the average rate of infection from the spread of corona virus endemic in a certain city daily is 2. Assume a suitable distribution to model the process.

b) Write a matlab program for model the probability of infection for the next 15 days.

c) Run as simulated plot for the Probability distribution and Cumulative distribution from the program above.

d) Using Simulation model estimate the probability that 3 people will infected in the next two days.

QUESTION 2

a) i) Based on a graph of the probability distribution (Q1d) indicate the probability that 3 persons will contract the virus in a given day

ii) Find the mean and standard deviation of the number of infections from (Q1) in the past three days.

b) The recent global climate change has necessitated the need for a new model for predicting weather patterns. Two scientists who were modeling this process in Ghana ended up with two different system models.

i) What could be the possible reason(s) for the differences in their system model? Justify your answer.

ii) In relation to real world data from the process how can you select the best model to employ for subsequent simulations and prediction of the process?

QUESTION 3

We wish to model the blood type of a person. It is known that blood type is inherited. If both parents carry genes for the AS and AS blood types, each child has probability 0.3 of getting two S genes and so of having blood type SS. Different children inherit independently of each other.

a) Write a Matlab program to determine the probability that the first child these parents have with type SS blood is their fifth child.

b) In relation to the three classifications of mathematical models, discuss the given genetic modelling problem in 2(a).

c) The administration of the Kasoa Government hospital wants to improve its quality of service by reducing the waiting time of travelers. For that purpose, they want to design what could be the best queuing strategy to have the minimum waiting time. You have been task to advice on the best queuing strategy in order to reduce the waiting time of patients before attended to. Discuss how you will address the problem

Code in C++

Objectives

• Use STL vector to create a wrapper class.

Create Class: Planet

Planet will be a simple class consisting of three fields:

• name: string representing the name of a planet, such as “Mars”
• madeOf: string representing the main element of the planet
• alienPopulation: int representing if the number of aliens living on the planet

Your Planet class should have the following methods:

• Planet(name, madeOf, alienPopulation) // Constructor
• getName(): string // Returns a planet’s name
• getMadeOf(): String // Returns a planet’s main element
• getAlienPopulation(): int // Returns a planet’s Aliens’ population

The constructor should throw an error if any of the following are true:

• The name is an empty string.
• The madeOf is an empty string
• The alienPopulation is less than zero

Here’s something important to remember: no methods should use standard input or output. They should neither pause to read in input or display any output. While you can include iostream for debugging purposes, your final file that you submit should not include the header.

Create Wrapper Class: Planets

Write a wrapper class for a listing of planets. This wrapper class will maintain a list of all planets and will return which planet has the highest number of Aliens. A wrapper class is a class that acts as decoration for another class (in this case, class vector from the STL). There’s only one field to this class:

• planets: vector of type Planet

Your Planets should have the following methods:

• addPlanet(Planet): void // Adds a planet to the listing of planets
• getCount(): int // Returns the number of planets currently in this data structure
• getMostPopulatedPlanet(): planet // Returns the planet with the highest number of aliens. If there is a tie among multiple planets, return the planet that was entered first. If the list is empty, throw an error.
• get(int i): planet // Returns the planet which is at position i.

Create the Driver Application

Create a driver application that demonstrates that each of the components of your program work. Create an empty planets structure with which to work. Create an interactive menu that gives the user the following choices and then performs that choice:

• Add Planet. The program will prompt the user for a name, a madeOf, and a alienPopulation. The program will create that object and pass it to the data structure via a call to addPlanet.
• Get count. Prints to the screen the number of planets in the data structure.
• Get the most populated planet. Prints to the screen the name, madeOf, and number of aliens of the current most populated planet in the data structure.
• Quit. Quits the application.

Tips for Everyone

• In your Driver application, try to make everything a function.
  • Reading in a planet name should be a function.
  • Reading in a planet’s madeOf should be a function.
  • Reading in a planet’s alienPopulation should be a function.
  • Building a planet should be a function.
  • Requesting a new planet and adding to a vector of planets should be a function.

Functions should be short: no longer than 20 lines. If something is longer than 20 lines, turn that into multiple functions, where each function does something slighly different. You will probably have more than 5 functions in this assignment.

Assignment 1 test Scenario

1. Create three planets as following

2. Then call the getMostPopulatedPlanet() method: It must return the “P2” planet. Print the name of that planet by calling the getName() method.

Output must look like: the most populated Planet is: P2 with 54000 aliens that is made of Silver

3. Call the getCount() method and print the returned value (output)

Output must look like: Number of Planet(s): 3

4. Call the getAlienPopulation() for planet P3 and print the returned value (output)

Output Must look like: The population of planet P3 is: 30000

Note that the underscored values must be read from the objects.

Array of Hope! Write code for a Java class ArrayPair with the following fields and methods: ArrayPair - arr1 [] : int - arr2 [] : int Fields - length1 : int - length2 : int + ArrayPair (int arraySize) Methods + add (int arrNumber, int value) : void + remove (int arrNumber) : void + equal () : boolean + greater () : boolean + print () : void Thus, there are two arrays of integers in the class with associated lengths (number of elements in each array).

Methods: ArrayPair: Constructor, instantiates the two arrays with the given size as a parameter. Sets the private lengths equal to zero since the arrays are initially empty. The constructor should not print or read anything.

add: Adds the given value to the right end of the array specified by the arrNumber (if equal to 1, adds to the arr1, if 2 adds to arr2, otherwise prints an error message and does not add the value). add should not print anything other than the error message when appropriate.

remove: Removes the rightmost element of the array specified by arrNumber. If the array is empty, an error message should be printed. remove should not print anything other than an error message when appropriate.

equal: Returns true if the two arrays have the same number of values and the exact same values in the same order. Otherwise, equal should return false. equal should not print anything to output.

greater: greater returns true if arr1 has more elements than arr2. greater returns false if arr2 has more elements than arr1. If the two arrays have the same number of elements, compare corresponding elements in the two arrays. For the first non-equal pair of values: if the arr1 value is greater than the arr2 value, true is returned; if the arr2 value is greater than the arr1 value, false is returned. If all the values are equal, false is returned.

print: Prints the values in both of the arrays with labels.

Main Program (Java class PairApp) Program first creates an ArrayPair object. The program then repeatedly reads commands of add, remove, equal, greater, print, or quit, until the user enters quit. If the user enters: add: Prompts the user for array number and value and calls add method to add that value to the given array. remove: Prompts the user for array number and calls the remove method to remove that element from the given array. equal: Calls equal method and prints whether or not the two arrays are equal. greater: Calls greater method prints whether or the not the first array is greater than the second. print: Calls print to print the values in the arrays. Note these further requirements: • User options should be accepted as uppercase or lowercase. • An error message is printed for an illegal choice. • The program should print an ending message when stopping. There is a sample run on the next page. Your output should follow the given text and spacing. Include a header comment describing the program and comment all variables, control structures and methods in the program.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 54.0 kg and standard deviation σ = 8.5 kg. Suppose a doe that weighs less than 45 kg is considered undernourished. (a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.) (b) If the park has about 2400 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does (c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 51 kg. If the average weight is less than 51 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 70 does is less than 51 kg (assuming a healthy population)? (Round your answer to four decimal places.) (d) Compute the probability that x < 56 kg for 70 does (assume a healthy population). (Round your answer to four decimal places.) Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was x = 56 kg. Do you think the doe population is undernourished or not? Explain. Since the sample average is below the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished. Since the sample average is above the mean, it is quite likely that the doe population is undernourished. Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 61.0 kg and standard deviation σ = 7.2 kg. Suppose a doe that weighs less than 52 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 58 kg. If the average weight is less than 58 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weightx for a random sample of 40 does is less than 58 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that x < 62.7 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was x= 62.7 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.    

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean ? = 64.0 kg and standard deviation ? = 8.3 kg. Suppose a doe that weighs less than 55 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2200 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 60 does should be more than 61 kg. If the average weight is less than 61 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight  x for a random sample of 60 does is less than 61 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that  x < 65 kg for 60 does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 60 does in December, and the average weight was  x = 65 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.    

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.