Friends Mercedes and Kaandra are working out together at the 400 m track. Kaandra can do the 1600 m in a blazing 5 minutes and 30 seconds. Mercedes is significantly slower doing that distance in 7 minutes. The women decide to have a race going twice around the track. To make it more competitive Kaandra gives Mercedes a 100 m head start (i.e. Mercedes only runs 700 m). Who wins, by how much time?

Rob and Candice are a married couple who live in Wisconsin and after 12 years of marriage have decided to divorce. Candice moves to Detroit and files for divorce and is granted it. Under the terms of the divorce Candice will be given the family home in Wisconsin as well as the family car. Rob believes that the home and car are his because he still lives in it and drives the car. Rob files a lawsuit in Wisconsin to have the state of Wisconsin declare ownership. Who wins and why?

**Question 4**: Three identical-looking chests contain the following booty:

1) 40 gold coins, 20 silver, and 40 bronze
2) 20 gold coins, 70 silver, and 10 bronze
3) 10 gold coins, 20 silver, and 70 bronze

Each chest is locked, but all have a small slit at the top where you could deposit additional coins (and maybe shake out a coin already inside). You select one of the chests at random, pick it up, and shake it. Out of the slit comes a gold coin, then after further shaking a bronze coin. Let's find the probability that you are holding chest 1.

a) Before any coins fall out, what is the prior probability that you you are holding chest 1?

**Response:**

b) If you indeed had chest 1, what is the probability that a gold coin would fall out, followed by a bronze coin?

**Response:**

c) If you instead had chest 2, what is the probability that a gold coin would fall out, followed by a bronze coin?

**Response:**

d) If you instead had chest 3, what is the probability that a gold coin would fall out, followed by a bronze coin?

**Response:**

e) What is the (unconditional) probability of shaking a chest (that was picked at random) and having a gold coin fall out followed by a bronze coin. Show your numerical calculation in the R chunk below. Sanity check: between 8-9%.

**Response:**

**Question 5** You look at 50000 past transactions of a convenience store. 225 had a chocolate bar. 489 had gum. 112 had both.

a. You pick one transaction at random from this list to audit. What's the probability that gum was part of this transaction?

**Response:**

b. The first item listed on the receipt of the transaction you picked turns out to be a chocolate bar. Now what's the probability that gum was part of this transaction?

**Response:**

c. What's the "lift" of the association between gum and chocolate bars? Explain what this number means in simple terms (there's multiple ways of interpreting this number; you only need to provide one).

**Response:**

(a)

Suppose our consumer has two possible consumption bundles, one with 1 unit of

clothes and 5 units of food, the second with 3 units of clothes and 4 units of food. For

which is the MRS of clothes for food the highest?

(b)

For the example in (a), what property of indifference curves tells us which will have the

highest MRS of clothes for food?

(c)

Suppose your income is $100. The price of food is $15, and the price of clothes is $20.

Draw your budget constraint labeling the two endpoints.

(d)

Suppose that you income in question 3 rises to $150, draw your new budget constraint.

(e)

Draw the highest indifference curve obtainable in questions 3 and 4. What principle are

you illustrating?

Consider three stock funds, which we will call Stock Funds 1, 2, and 3. Suppose that Stock Fund 1 has a mean yearly return of 8.00 percent with a standard deviation of 16.30 percent; Stock Fund 2 has a mean yearly return of 11.40 percent with a standard deviation of 18.80 percent, and Stock Fund 3 has a mean yearly return of 13.10 percent with a standard deviation of 8.90 percent.

(a) For each fund, find an interval in which you would expect 95.44 percent of all yearly returns to fall. Assume returns are normally distributed. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

(b) Using the intervals you computed in part a, compare the three funds with respect to average yearly returns and with respect to variability of returns.

(c) Calculate the coefficient of variation for each fund, and use your results to compare the funds with respect to risk. Which fund is riskiest? (Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Fund 1 is  (Click to select)  second riskiest  least risky  riskiest  , Fund 2 is  (Click to select)  least risky  riskiest  second riskiest  and Fund 3 is  (Click to select)  riskiest  second riskiest  least risky  .

2. In humans, fingerprint ridge count follows a polygenic inheritance pattern. The minimum number of ridges is 80 in males and 70 in females. Each active allele will produce an additional 12 ridges in males and 9 ridges in females. Active alleles are represented by uppercase letters.

• What is the fingerprint ridge count in a male having the following genotype? o AABBccDd? __________ aabBccdd ____________

• What is the fingerprint ridge count in a female having the following genotype? o AABBCCDD?_________ aabbCcDD?____________

• What is the least number of active alleles a child born of the following couple could inherit? Father: AABBccDD Mother: aabbCCdd • What is the probability that a child would have a genotype with the least number of active alleles?

3. The gene for sickle cell anemia is recessive. Suppose a man and woman are both carriers.

• What is the probability that they will have a child with normal blood cells?

• What is the probability that they will have a child who has sickle cell anemia?

• What is the probability that they will have a child who is a carrier?

4. A woman with type A- blood marries a man with type B+ blood. Is it possible for this couple to have a child with:

• Type O blood?

• Type AB blood?

• Type A blood?

• Type B blood?

5. Hair texture in humans is presumed to follow an incomplete dominance inheritance pattern whereby genotype CC results in curly hair, cc results in straight hair, and Cc results in wavy hair. Suppose a man with straight hair has children with a woman who has wavy hair. What is the probability that a child born to this couple will have:

• Straight hair?

• Wavy hair?

• Curly hair?

6. The production of coat color in Labrador retrievers involves two sets of genes where one set is epistatic to the other. Suppose the gene for black (B) fur is dominant to brown (b) fur, and the production of coat pigment requires at least one copy of the dominant gene, E. Lack of coat pigment (ee) results in a yellow lab. A cross is made between two dogs with genotype, BbEe. Which color dog would be most rare?

*Need all questions answered*

Outcomes: • Write a Java program that implements linked list algorithms

can u also show thee testing code

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

This is the starter code

import java.util.NoSuchElementException;

// Put your prologue comments here

public class LinkedAlgorithms {

  
   private class Node {
       private String data;
       private Node next;

       private Node(String data) {
           this.data = data;
           this.next = null;
       }
   }

   public Node head;
   public int numItems;

   /**
   * Creates the empty list.
   */
   public LinkedAlgorithms() {
   }

   /**
   * Creates a list containing all the elements of the passed array.
   * {@code data[0]} will be the first element of the list, {@code data[1]} will
   * be the second element of the list, and so on.
   *
   * @param data The array of values
   * @throws NullPointerException - data is null
   */
   public LinkedAlgorithms(String[] data) {
   }

   /**
   * Constructs a deep copy of the linked list {@code original}
   *
   * @param original The list to be copied
   * @throws NullPointerException - original is null
   */
   public LinkedAlgorithms(LinkedAlgorithms original) {
   }

   /**
   * Returns array with all the elements.
   *
   * @return Array containing all elements.
   */
   public String[] toArray() {
       return null;
   }

   /**
   * Formats the elements in the list using leading and ending brackets (i.e., []), with the values comma separated.
   * There will be one space between each of these but none at the beginning nor at the end.
   * Some examples:
   * if the list is empty, toString() gives []
   * if the list has these three elements in this order: "hello", "world", "everyone", then the result should be
   * [hello, world, everyone]
   */
   @Override
   public String toString() {
       return null;
   }

   /**
   * Returns the number of items in the list
   *
   * @return Number of items in the list
   */
   public int size() {
       return 0;
   }

   /**
   * Determines if two lists contain exactly the same values, in exactly the same
   * order.
   *
   * @return {@code true} if and only if obj is an list that is equivalent to the
   * incoming list.
   */
   public boolean equalsLinkedList(LinkedAlgorithms obj) {
       return false;
   }

   /**
   * Determines if {@code key} is in the linked list.
   *
   * @param key The value to be found
   * @return true if and only if {@code key} is in the list
   */
   public boolean contains(String key) {
       return false;
   }

   /**
   * Determines the index of {@code key}. -1 is returned if the value is not
   * present in the linked list. If {@code key} is present present more than once,
   * the first index is returned.
   *
   * @param key The value to be found
   * @return The index of the {@code key}
   */
   public int find(String key) {
       return 0;
   }

   /**
   * Returns the value of the first element of the list.
   *
   * @return The first element of the list.
   * @throws NoSuchElementException the list is empty
   */
   public String getFirst() {
       return null;
   }

   /**
   * Returns the value of the last element of the list.
   *
   * @return The last element of the list.
   * @throws NoSuchElementException the list is empty
   */
   public String getLast() {
       return null;
   }

   /**
   * Returns the value of the {@code ith} element of the list (0 based).
   *
   * @param i The target index
   * @return The value of the ith element of the list.
   * @throws IndexOutOfBoundsException {@code i} is illegal
   */
   public String getAt(int i) {
       return null;
   }

   /**
   * Adds {@code data} to the beginning of the list. All other values in the list
   * remain but they are "shifted to the right."
   *
   * @param data The value to add to the list
   */
   public void insertFirst(String data) {
   }

   /**
   * Adds {@code data} to the end of the list. All other values in the list remain
   * in their current positions.
   *
   * @param data The value to add to the list
   */
   public void insertLast(String data) {
   }

   /**
   * Adds data to a specific spot in the list. The values in the list remain
   * intact but {@code data} is inserted in the list at position {@code i}. When
   * {@code i=0}, the result is the same as {@code insertFirst}.
   *
   * @param i The target index
   * @param data The value to add to the list
   * @throws IndexOutOfBoundsException {@code i} is illegal
   */
   public void insertAt(int i, String data) {
   }

   /**
   * Adds {@code newData} the position immediately preceding {@code existingData}.
   * If the {@code existingData} appears multiple times, only the first one is
   * used.
   *
   * @param newData The value to add to the list
   * @param existingData The value used to control where insertion is to take
   * place
   * @throws NoSuchElementException {@code existingData} is not in the list
   */
   public void insertBefore(String newData, String existingData) {
   }

   /**
   * Adds {@code newData} the position immediately after {@code existingData}. If
   * the {@code existingData} appears multiple times, only the first one is used.
   *
   * @param newData The value to add to the list
   * @param existingData The value used to control where insertion is to take
   * place
   * @throws NoSuchElementException {@code existingData} is not in the list
   */
   public void insertAfter(String newData, String existingData) {
   }

   /**
   * Removes the first element of the list. The remaining elements are kept in
   * their existing order.
   *
   * @return The value removed from the list
   * @throws NoSuchElementException if the list is empty.
   */
   public String removeFirst() {
       return null;
   }

   /**
   * Removes the last element of the list. The remaining elements are kept in
   * their existing order.
   *
   * @return The value removed from the list
   * @throws NoSuchElementException if the list is empty.
   */
   public String removeLast() {
       return null;
   }

   /**
   * Removes the ith element of the list. The remaining elements are kept in their
   * existing order.
   *
   * @param i The target index
   * @return The value removed from the list
   * @throws IndexOutOfBoundsException i does not represent a legal index
   */
   public String removeAt(int i) {
       return null;
   }

   /**
   * Removes the first occurrence of data in the linked list.
   *
   * @param data The value to be removed.
   * @return {@code true} if and only if {@code data} was removed
   */
   public boolean removeFirstOccurrenceOf(String data) {
       return false;
   }

   /**
   * Removes the all occurrence of {@code data} in the linked list.
   *
   * @param data The value to be removed.
   * @return The number of times {@code data} was removed
   */
   public int removeAllOccurrencesOf(String data) {
       return 0;
   }

   /**
   * Reverses the elements in the incoming linked list.
   */
   public void reverse() {
   }

   /**
   * Puts all the elements in the list to uppercase.
   */
   public void toUpper() {
   }

   /**
   * Returns the concatenation of all strings, from left to right. No extra spaces
   * are inserted.
   *
   * @return Concatenation of all string in the list
   */
   public String getConcatenation() {
       return null;
   }

   /**
   * Returns the alphabetically last value in the list.
   *
   * @return The alphabetically last value in the list
   * @throws NoSuchElementException list is empty
   */
   public String getAlphabeticallyLast() {
       return null;
   }

   /**
   * Returns the index where the alphabetically last value value resides. If this
   * value appears multiple times, the first occurrence is used.
   *
   * @return Index value of where maximum value resides
   * @throws NoSuchElementException list is empty
   */
   public int indexOfAlphabeticallyLast() {
       return 0;
   }

   /*
   * Determines if the two list contain elements that have exactly the same
   * value, with the same list sizes, but with the elements perhaps in different order.
   *
   * @returns true only if the two lists are permutations of one another.
   */
   public boolean anagrams(LinkedAlgorithms other) {
       return false;
   }

   public static void main(String[] args) {
       String[] items = { "hello", "world" };
       LinkedAlgorithms LL1 = new LinkedAlgorithms();
       LinkedAlgorithms LL2 = new LinkedAlgorithms(items);
       LinkedAlgorithms LL3 = new LinkedAlgorithms(LL1);
   }
}

Question:1

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 67 and estimated standard deviation σ = 40. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

The probability distribution of x is approximately normal with μ_x = 67 and σ_x = 40.The probability distribution of x is approximately normal with μ_x = 67 and σ_x = 28.28.    The probability distribution of x is approximately normal with μ_x = 67 and σ_x = 20.00.The probability distribution of x is not normal.

What is the probability that x < 40? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)


(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?

Yes or No    

Explain what this might imply if you were a doctor or a nurse.

The more tests a patient completes, the stronger is the evidence for excess insulin.The more tests a patient completes, the weaker is the evidence for excess insulin.    The more tests a patient completes, the stronger is the evidence for lack of insulin.The more tests a patient completes, the weaker is the evidence for lack of insulin.

Question 2:

certain mutual fund invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the fund. Assume x has mean μ = 1.7% and standard deviation σ = 0.7%.

(a) The fund has over 350 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 350 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2.

The random variable  ---Select--- x-bar x is a mean of a sample size n = 350. By the  ---Select--- theory of normality law of large numbers central limit theorem , the  ---Select--- x x-bar distribution is approximately normal.

(b) After 6 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has a normal distribution as based on part (a). (Round your answer to four decimal places.)


(c) After 2 years, what is the probability that 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?

YesNo    

Why would this happen?

The standard deviation  ---Select--- increases decreases stays the same as the  ---Select--- average sample size mean distribution increases.

(e) If after 2 years the average monthly percentage return was less than 1%, would that tend to shake your confidence in the statement that μ = 1.7%? Might you suspect that μ has slipped below 1.7%? Explain.

This is very unlikely if μ = 1.7%. One would not suspect that μ has slipped below 1.7%.This is very unlikely if μ = 1.7%. One would suspect that μ has slipped below 1.7%.    This is very likely if μ = 1.7%. One would suspect that μ has slipped below 1.7%.This is very likely if μ = 1.7%. One would not suspect that μ has slipped below 1.7%.

Question 3:

It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that x has a normal distribution with μ = 12 feet per year and σ = 4.5 feet per year.

Under the influence of prevailing wind patterns, what is the probability of each of the following? (Round your answers to four decimal places.)

(a) an escape dune will move a total distance of more than 90 feet in 10 years


(b) an escape dune will move a total distance of less than 80 feet in 10 years


(c) an escape dune will move a total distance of between 80 and 90 feet in 10 years

A basketball player makes 64% of her free throw attempts. Suppose she is awarded 3 free throws during a play, and let X be the number of free throws she makes during this trial. Complete the following probability distribution table. Round the probabilities to 3 decimals.

A basketball player makes 60% of his shots from the free throw line. Suppose that each of his shots can be considered independent and that he takes 4 shots. Let X = the number of shots that he makes. What is the probability that he makes all 4 shots?