The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.9 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. What is the median recovery time? days

c. What is the Z-score for a patient that took 4.4 days to recover?

d. What is the probability of spending more than 2.5 days in recovery?

e. What is the probability of spending between 2.9 and 3.7 days in recovery?

f. The 90th percentile for recovery times is days.

Private nonprofit four-year colleges charge, on average, $27,166 per year in tuition and fees. The standard deviation is $7,402. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 25,605 per year.

c. Find the 60th percentile for this distribution. $ (Round to the nearest dollar.)

The average number of words in a romance novel is 64,416 and the standard deviation is 17,228. Assume the distribution is normal. Let X be the number of words in a randomly selected romance novel. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the proportion of all novels that are between 59,248 and 71,308 words.

c. The 80th percentile for novels is words. (Round to the nearest word)

d. The middle 50% of romance novels have from words to words. (Round to the nearest word)

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.4 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that the person is between 59.3 and 61.7 inches.

c. The middle 40% of Martian heights lie between what two numbers?
Low: inches
High: inches

Problem 2: Valuation on a Multiplicative Binomial Lattice

This problem reviews some of the main ideas of valuation on a binomial lattice and the properties of put and call options. You may wish to review the relevant lecture material and readings.

Suppose that the price of a share of KAF stock is S(0) = £120 in period 0. At the beginning of period 1, the price of a share can either move upward to S(1) = u S(0) or downward to S(1) = d S(0). Suppose that u = 4/3 = 1.333 and d = 3/4 = .75, so that S(1) = u S(0) = £160 after an up move and S(1) = d S(0) = £90 after a down move. Suppose that the probability of an up move is p = 0.5.

Similarly, suppose that, at the beginning of period 2, the share price either moves up or down by the same multiplicative factors and with the same probability (0.5) of an up move. (If the probability of an up move in a period is 0.5, then the probability of a down move in a period is also 0.5.) Hence, if the share price in period 1 is S(1), then the share price at the beginning of period 2 is either S(2) = u S(1) = 4/3 S(1) or S(2) = d S(1) = 3/4 S(1).

For simplicity, suppose that a period is a year, and let the riskless interest rate be r = .12, that is, 12% per period.

2. (i) Briefly explain what is meant by an Arrow-Debreu 1-period-ahead down security and the 1-period-ahead down state price.

(ii) Write down two equations that describe a replicating portfolio of KAF shares and riskless bonds that has a payoff of 1 in period 1 if the price of a KAF share moves downward at the beginning of period 1 and has a payoff of 0 otherwise. Briefly explain your reasoning.

Calculate the number of shares of KAF stock and the amount of riskless bonds in the replicating portfolio.

(Recall that buying riskless bonds is equivalent to lending money at the riskless rate of interest and selling riskless bonds short is equivalent to borrowing money at the riskless rate. A negative number of shares in a portfolio corresponds to selling those shares short.)

In Java: Initiate empty queue of strings and recreate .isempty, .size, .dequeue, .enqueue methods.

//You may not use the original methods of the stack api to answer. You may not add any more fields to the class.

import java.util.NoSuchElementException;

import edu.princeton.cs.algs4.Stack;

public class StringQueue {
   //You may NOT add any more fields to this class.
   private Stack stack1;
   private Stack stack2;

   /**
   * Initialize an empty queue.
   */
   public StringQueue() {

//TODO
   }

   /**
   * Returns true if this queue is empty.
   *
   * @return {@code true} if this queue is empty; {@code false} otherwise
   */
   public boolean isEmpty() {
       //TODO
   }

   /**
   * Returns the number of items in this queue.
   *
   * @return the number of items in this queue
   */
   public int size() {
       // TODO
   }

   /**
   * Adds the item to this queue.
   *
   * @param item the item to add
   */
   public void enqueue(String item) {
       // TODO
   }

   /**
   * Removes and returns the item on this queue that was least recently added.
   *
   * @return the item on this queue that was least recently added
   * @throws NoSuchElementException if the queue is empty
   */
   public String dequeue() throws NoSuchElementException {
       // TODO
   }
}

Hints:
You will need to store enqueued items on one of the stacks. However, when it comes time to dequeue, those items will be in the wrong order, so use the second stack to reverse the order. Note that once the items are in the second stack, they will come out of the second stack in the correct order and you can still use the first stack to store new items that are enqueued. You should not keep moving the strings back and forth between the two stacks as this will make your solution extremely inefficient. Each string should be inserted into stack1 and most once and into stack2 at most once.
I suggest you start with the very simple sequence: enqueue(“one”), enqueuer(“two”), dequeue(), dequeue(). Of course, the String “one” should come out first followed by the String “two”. Once you have that working, start testing your code with more complex sequences and fixing any use cases you missed in your original attempt at a solution. For example, make sure to at least try the seuquence enqueue(“one”), enqueuer(“two”), dequeue(), enqueue(“three”), dequeue(), dequeue().

10. You have researched information on 3 mutual funds. If the risk-free rate is currently 5.5%, which one of these
funds has managed the best risk-adjusted performance?

Fund Q:
Average annual return: 8.21%
Standard deviation: 7.00%
Beta coefficient: 0.921
Fund R:
Average annual return: 11.55%
Standard deviation: 13.52%
Beta coefficient: 1.100
Fund S:
Average annual return: 12.00%
Standard deviation: 16.05%
Beta coefficient: 1.825
A. Fund S, because it has the highest Treynor ratio
B. Fund R, because it has the highest Sharpe ratio
C. Fund S, because it has the highest rate of return
D. Fund Q, because it has the lowest standard deviation

11. Based on the following information, calculate the expected rate of return for Softco Corporation.
Stock’s beta: 0.80
Forecasted market rate of return: 15%
Risk-free rate of return: 6.5%
A. 6.80%
B. 8.50%
C. 13.30%
D. 17.20%

12. You have determined Stock A has a beta of +1.56, and the market is expected to decline 10% over the next
year. Using security market line analysis, calculate the percentage you expect the return of Stock A to rise or
fall over the next year.
A. Fall by 1.56%
B. Fall by 15.6%
C. Rise by 1.56%
D. Rise by 156%

13. Consider the following information regarding 2 possible investments: Stocks J and K.
Stock J:
Expected return: 11.5%
Standard deviation: 8%
Stock K:
Expected return: 8.2%
Standard deviation: 6%

Identify which of these investments you would prefer and why.
A. Stock K, because it has the least risk
B. Stock J, because it has the highest expected return
C. Stock J, because it has the lowest coefficient of variation
D. Stock K, because it has the highest coefficient of variation

14. A call option with an exercise price of $105 is selling in the open market for $4.25 when the market price of
the underlying stock is $102. Calculate the intrinsic value of this option.
A. –$3.00
B. $0
C. $3.00
D. $4.25

15. Angela purchased a corporate bond currently selling for $925 in the secondary market. The bond has a coupon
rate of 7.75% and matures in 12 years. Calculate the yield to maturity on this bond.
A. 4.39%
B. 8.49%
C. 8.77%
D. 15.50%

Identify the Distribution

Select the Distribution that best fits the definition of the random variable X in each case.

Question 1) You have 5 cards in a pile, including one special card. You draw 3 cards one at a time without replacement. X = the number of non-special cards drawn.

Question 2) The number of car accidents at a particular intersection occur independently at a constant rate with no chance of two occurring at exactly the same time. X = the number of accidents on a Thursday.

Question 3) A soccer player has a certain probability p of being injured in each game, independently of other games. X = the number of games played before the player is injured.

Question 4) A jury of 12 people each independently vote on whether a defendant is guilty or not guilty, each with the same probability. X = the number who vote guilty.

Question 5) In a single game of (American) roulette, a small ball is rolled around a spinning wheel in such a way that it is equally likely to land in any of 38 bins. Sixteen of the bins are Red, another 16 are Black, and the remaining 2 are Green. Suppose 5 games of roulette are to be played. What is the joint distribution of the number of times the ball lands Red and the number of times the ball lands Green?

Question 6) Each hurricane independently has a certain probability of being classified as "serious." A climatologist wants to study the effects of the next 5 serious hurricanes. X = the number of non-serious hurricanes observed until the data is collected.

Question 7) The amount of anesthetic required to keep a person asleep during a 1-hour surgery is directly related to their weight. A hospital is performing 10 such surgeries on 10 independent patients. X = the total amount of anesthetic required.

Question 8) To measure the concentration of chemicals in rain, a square of absorbant paper is placed outside in a rainstorm for a few seconds, where raindrops are equally likely to land anywhere on it. X = the x-coordinate of a random raindrop on the paper.

Question 9) In Lotto 6/49 a player selects a set of six numbers (with no repeats) from the set {1, 2, ..., 49}. In the lottery draw, six numbers are selected at random. Let X = the first number drawn.

Question 10) Emails arrive at a server independently of each other at the uniform rate throughout the day with little chances of more than one email arriving at the same instant. X = time between two consecutive emails.

Problem 7-18 Activity-Based Costing and Bidding on Jobs [LO7-2, LO7-3, LO7-4]

Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the company’s estimator and the work supervisors. The on-site supervisors claim that the estimators do not adequately distinguish between routine work, such as removal of asbestos insulation around heating pipes in older homes, and nonroutine work, such as removing asbestos-contaminated ceiling plaster in industrial buildings. The on-site supervisors believe that nonroutine work is far more expensive than routine work and should bear higher customer charges. The estimator sums up his position in this way: “My job is to measure the area to be cleared of asbestos. As directed by top management, I simply multiply the square footage by $3.60 to determine the bid price. Since our average cost is only $2.775 per square foot, that leaves enough cushion to take care of the additional costs of nonroutine work that shows up. Besides, it is difficult to know what is routine or not routine until you actually start tearing things apart.”

To shed light on this controversy, the company initiated an activity-based costing study of all of its costs. Data from the activity-based costing system follow:

Required:

1. Perform the first-stage allocation of costs to the activity cost pools.

2. Compute the activity rates for the activity cost pools.

3. Using the activity rates you have computed, determine the total cost and the average cost per thousand square feet of each of the following jobs according to the activity-based costing system.

a. A routine 1,000-square-foot asbestos removal job.

b. A routine 2,000-square-foot asbestos removal job.

c. A nonroutine 2,000-square-foot asbestos removal job.

Problem 7-18 Activity-Based Costing and Bidding on Jobs [LO7-2, LO7-3, LO7-4]

Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the company’s estimator and the work supervisors. The on-site supervisors claim that the estimators do not adequately distinguish between routine work, such as removal of asbestos insulation around heating pipes in older homes, and nonroutine work, such as removing asbestos-contaminated ceiling plaster in industrial buildings. The on-site supervisors believe that nonroutine work is far more expensive than routine work and should bear higher customer charges. The estimator sums up his position in this way: “My job is to measure the area to be cleared of asbestos. As directed by top management, I simply multiply the square footage by $3.20 to determine the bid price. Since our average cost is only $2.81 per square foot, that leaves enough cushion to take care of the additional costs of nonroutine work that shows up. Besides, it is difficult to know what is routine or not routine until you actually start tearing things apart.”

To shed light on this controversy, the company initiated an activity-based costing study of all of its costs. Data from the activity-based costing system follow:

Required:

1. Perform the first-stage allocation of costs to the activity cost pools.

2. Compute the activity rates for the activity cost pools.

3. Using the activity rates you have computed, determine the total cost and the average cost per thousand square feet of each of the following jobs according to the activity-based costing system.

a. A routine 1,000-square-foot asbestos removal job.

b. A routine 2,000-square-foot asbestos removal job.

c. A nonroutine 2,000-square-foot asbestos removal job.

Problem 7-18 Activity-Based Costing and Bidding on Jobs [LO7-2, LO7-3, LO7-4]

Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the company’s estimator and the work supervisors. The on-site supervisors claim that the estimators do not adequately distinguish between routine work, such as removal of asbestos insulation around heating pipes in older homes, and nonroutine work, such as removing asbestos-contaminated ceiling plaster in industrial buildings. The on-site supervisors believe that nonroutine work is far more expensive than routine work and should bear higher customer charges. The estimator sums up his position in this way: “My job is to measure the area to be cleared of asbestos. As directed by top management, I simply multiply the square footage by $2.70 to determine the bid price. Since our average cost is only $2.40 per square foot, that leaves enough cushion to take care of the additional costs of nonroutine work that shows up. Besides, it is difficult to know what is routine or not routine until you actually start tearing things apart.”

To shed light on this controversy, the company initiated an activity-based costing study of all of its costs. Data from the activity-based costing system follow:

Required:

1. Perform the first-stage allocation of costs to the activity cost pools.

2. Compute the activity rates for the activity cost pools.

3. Using the activity rates you have computed, determine the total cost and the average cost per thousand square feet of each of the following jobs according to the activity-based costing system.

a. A routine 1,000-square-foot asbestos removal job.

b. A routine 2,000-square-foot asbestos removal job.

c. A nonroutine 2,000-square-foot asbestos removal job.

Problem 7-18 Activity-Based Costing and Bidding on Jobs [LO7-2, LO7-3, LO7-4]

Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the company’s estimator and the work supervisors. The on-site supervisors claim that the estimators do not adequately distinguish between routine work, such as removal of asbestos insulation around heating pipes in older homes, and nonroutine work, such as removing asbestos-contaminated ceiling plaster in industrial buildings. The on-site supervisors believe that nonroutine work is far more expensive than routine work and should bear higher customer charges. The estimator sums up his position in this way: “My job is to measure the area to be cleared of asbestos. As directed by top management, I simply multiply the square footage by $2.80 to determine the bid price. Since our average cost is only $2.575 per square foot, that leaves enough cushion to take care of the additional costs of nonroutine work that shows up. Besides, it is difficult to know what is routine or not routine until you actually start tearing things apart.”

To shed light on this controversy, the company initiated an activity-based costing study of all of its costs. Data from the activity-based costing system follow:

Required:

1. Perform the first-stage allocation of costs to the activity cost pools.

2. Compute the activity rates for the activity cost pools.

3. Using the activity rates you have computed, determine the total cost and the average cost per thousand square feet of each of the following jobs according to the activity-based costing system.

a. A routine 1,000-square-foot asbestos removal job.

b. A routine 2,000-square-foot asbestos removal job.

c. A nonroutine 2,000-square-foot asbestos removal job.

In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. We number the lines with their distances from the left most vertical line (which serves as the y-axis).Each of our volunteers selects a line and stand facing it at close proximity to the board. Between the board and the volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks.

We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3)

These data represent a set of ordered pairs or a function. Since this function has an infinite number of ordered pairs, we are going to find an equation that defines this function. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis.

1. In this specific model of ball toss

    a) What does the x-axis represent?

    b) What do the x-coordinates represent?

    C) What do the y-coordinates represent?

2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each    square 10cm).Make sure you label the axis and the points.

3. Draw a smooth curve containing these points.

4. What shape does the graph have?

5. How does this shape open?

6. What kind of function this graph represents?

7. Write the standard form of the equation that represents this function.

8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7

    a) Find the quadratic polynomial that predicts y from x. (Hint: you should resolve a system of linear equation to find the coefficients of the equation). (Round your answers to the nearest ten thousandths). (Remember to show all your work)

b) Is the leading coefficient positive or negative?

    c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your work over before you continue).

9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth).

   b) What is the sign of this height?

   c) What is the position of the ball to the eraser tray?

   d) Write this ordered pairs and plot its point T on the graph.

10. a) At what values of x does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm)

      b) Display these points I and J on the graph and write their coordinates.

      c) What are these points called?

11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray?(Round your answers to the nearest cm)

     b) Write these ordered pairs and plot their points R and S on the graph.

12. a) At what distance from the y-axis was the ball at its highest point?(Round your answer to the nearest cm).

     b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm).

     c) What is the name of this highest point of the graph?

     d) Write the coordinate of the highest point V and plot it on the graph.

please answer q2, q3,24,q5,q6 and q11,q12