Note: You need to show your work. Microsoft Word has an equation editor. Go to “Insert” and “Equation” on newer versions of Word. On older versions, go to “Insert” and “Object” and “Microsoft Equation.” If you choose instead to use Excel for your calculations, be sure to upload your well-documented Excel files so that I can check your work, but you still need to answer the questions IN THIS FILE!

Chapter 5 Part A: A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. 1. Compute the probability that 2 or fewer will withdraw. 2. Compute the probability that exactly 4 will withdraw. 3. Compute the probability that more than 3 will withdraw. 4. Compute the expected number of withdrawals.

Chapter 5 Part B: Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. 1. Compute the probability of no arrivals in a one-minute period. 2. Compute the probability that three or fewer passengers arrive in a one-minute period. 3. Compute the probability of no arrivals in a 15-second period. 4. Compute the probability of at least one arrival in a 15-second period.

Question 1)

5 unrelated people donate blood at the red cross. If there is a 60% chance that a person has O blood type...

Part A. What is the probability they have at least one person with O blood type?
Part B. What is the probability they have at most two people with O blood type?
Part C. What is the expected number of people who will have O blood type?

Part D. If instead it was 500 unrelated people, what is the approximate probability that they have at least 310 people with O blood type?

Question 2)

Men heights are assumed to be normally distributed with mean 70 inches and standard deviation 4 inches.

Part A) What is the probability that a randomly selected man is between 65 and 68 inches tall?
Part B) What is the probability that a randomly selected man is less than 66 inches tall?

Part C) What is the minimum height of the top 10% of men?
Part D) What is the maximum height of the bottom 25% of men?
Part E) What is the probability that 4 randomly selected men have an average height less than 72 inches? Part F. What is the probability that 4 randomly selected men are all less than 72 inches in height?

Question 1:

A binomial distribution has p = 0.21 and n = 94. Use the normal approximation to the binomial distribution to answer parts (a) through (d) below. Round to four decimal places as needed.)

a. What are the mean and standard deviation for this distribution?

b. What is the probability of exactly 15 successes?

c. What is the probability of 13 to 21 successes?

d. What is the probability of 9 to 17 successes?

Question 2:

The average number of miles driven on a full tank of gas in a certain model car before its low-fuel light comes on is 331. Assume this mileage follows the normal distribution with a standard deviation of 44 miles. Complete parts a through d below. (Round to four decimal places as needed.)

1. What is the probability that, before the low-fuel light comes on, the car will travel less than 361 miles on the next tank of gas?
2. What is the probability that, before the low-fuel light comes on, the car will travel more than 280 miles on the next tank of gas?
3. What is the probability that, before the low-fuel light comes on, the car will travel between 301 and 321 miles on the next tank of gas?
4. What is the probability that, before the low-fuel light comes on, the car will travel exactly 353 miles on the next tank of gas?

(Round the final answer to 4 decimal digits) 1. A brand name has a 70% recognition rate. Assume the owner f the brand wants to verify that rate by begging with a small sample of 6 randomly select consumers. a. What is the probability that exactly 4 of the selected consumers recognize the brand name?

b. What is the probability that all of the selected consumers recognize the brand name?

c. What is the probability that at least 5 of the selected consumers recognize the brand name?

d. What is the probability that at most 2 of the selected consumers recognize the brand name?

2) . The lengths of pregnancies are normally distributed with a mean of 272 days and a standard deviation of 15 days. If 35 women are randomly selected, find the probability that they have a mean pregnancy between 271 days and 275 days.

3) The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.50° F. If 25 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° F.

4) The average number of pounds of red meat a person consumes each year is 190 with a standard deviation of 24 pounds (Source: American Dietetic Association). If a sample of 60 individuals is randomly selected, find the probability that the mean of the sample will be Less than 192 pounds.

Java the goal is to create a list class that uses an array to implement the interface below. I'm having trouble figuring out the remove(T element) and set(int index, T element). I haven't added any custom methods other than a simple expand method that doubles the size by 2. I would prefer it if you did not use any other custom methods. Please use Java Generics, Thank you.

import java.util.*;

/**
* Interface for an Iterable, Indexed, Unsorted List ADT.
* Iterators and ListIterators provided by the list are required
* to be "fail-fast" and throw ConcurrentModificationException if
* the iterator detects any change to the list from another source.
* Note: "Unsorted" only means that it is not inherently maintained
* in a sorted order. It may or may not be sorted.
*
* @author CS 221
*
* @param - class of objects stored in the list
*/
public interface IndexedUnsortedList extends Iterable
{
/**
* Adds the specified element to the front of this list.
*
* @param element the element to be added to the front of this list
*/
public void addToFront(T element);

/**
* Adds the specified element to the rear of this list.
*
* @param element the element to be added to the rear of this list
*/
public void addToRear(T element);

/**
* Adds the specified element to the rear of this list.
*
* @param element the element to be added to the rear of the list
*/
public void add(T element);

/**
* Adds the specified element after the specified target.
*
* @param element the element to be added after the target
* @param target the target is the item that the element will be added after
* @throws NoSuchElementException if target element is not in this list
*/
public void addAfter(T element, T target);
  
/**
* Inserts the specified element at the specified index.
*
* @param index the index into the array to which the element is to be inserted.
* @param element the element to be inserted into the array
* @throws IndexOutOfBoundsException if the index is out of range (index < 0 || index > size)
*/
public void add(int index, T element);

/**
* Removes and returns the first element from this list.
*
* @return the first element from this list
* @throws NoSuchElementException if list contains no elements
*/
public T removeFirst();

/**
* Removes and returns the last element from this list.
*
* @return the last element from this list
* @throws NoSuchElementException if list contains no elements
*/
public T removeLast();

/**
* Removes and returns the first element from the list matching the specified element.
*
* @param element the element to be removed from the list
* @return removed element
* @throws NoSuchElementException if element is not in this list
*/
public T remove(T element);

/**
* Removes and returns the element at the specified index.
*
* @param index the index of the element to be retrieved
* @return the element at the given index
* @throws IndexOutOfBoundsException if the index is out of range (index < 0 || index >= size)
*/
public T remove(int index);
  
/**
* Replace the element at the specified index with the given element.
*
* @param index the index of the element to replace
* @param element the replacement element to be set into the list
* @throws IndexOutOfBoundsException if the index is out of range (index < 0 || index >= size)
*/
public void set(int index, T element);

/**
* Returns a reference to the element at the specified index.
*
* @param index the index to which the reference is to be retrieved from
* @return the element at the specified index
* @throws IndexOutOfBoundsException if the index is out of range (index < 0 || index >= size)
*/
public T get(int index);

/**
* Returns the index of the first element from the list matching the specified element.
*
* @param element the element for the index is to be retrieved
* @return the integer index for this element or -1 if element is not in the list
*/
public int indexOf(T element);

/**
* Returns a reference to the first element in this list.
*
* @return a reference to the first element in this list
* @throws NoSuchElementException if list contains no elements
*/
public T first();

/**
* Returns a reference to the last element in this list.
*
* @return a reference to the last element in this list
* @throws NoSuchElementException if list contains no elements
*/
public T last();

/**
* Returns true if this list contains the specified target element.
*
* @param target the target that is being sought in the list
* @return true if the list contains this element, else false
*/
public boolean contains(T target);

/**
* Returns true if this list contains no elements.
*
* @return true if this list contains no elements
*/
public boolean isEmpty();

/**
* Returns the number of elements in this list.
*
* @return the integer representation of number of elements in this list
*/
public int size();

/**
* Returns a string representation of this list.
*
* @return a string representation of this list
*/
public String toString();

/**
* Returns an Iterator for the elements in this list.
*
* @return an Iterator over the elements in this list
*/
public Iterator iterator();

/**
* Returns a ListIterator for the elements in this list.
*
* @return a ListIterator over the elements in this list
*
* @throws UnsupportedOperationException if not implemented
*/
public ListIterator listIterator();

/**
* Returns a ListIterator for the elements in this list, with
* the iterator positioned before the specified index.
*
* @return a ListIterator over the elements in this list
*
* @throws UnsupportedOperationException if not implemented
*/
public ListIterator listIterator(int startingIndex);
}

1. You want to understand sampling distribution. The average number of children per woman is 2.2 with a standard deviation is .1. If you took a sample of 16 women, what is the probability that:
   1. The average of this group is less that 2.3?
   2. The average for this group is greater than 2.45?
   3. The average for this group lies between 2.15 and 2.4.                                                      (10)

You are not sure if the mean value is correct but you believe that the standard deviation is correct. You took a sample of 16 women and average number of children for this group is 2.4. Prepare a confidence Interval for the mean number of children for a woman.

2. When parking a car in a downtown parking lot, drivers pay according to the number of hours or parts thereof. The probability distribution of the number of hours that cars are parked has been estimated as follows:

X                  1        2        3        4        5        6        7        8

P(X)             .24     .18     .13     .10     .07     .04     .04     .20

a. Find the mean and standard deviation of the number of hours that cars are parked in the lot.

b. If the cost of parking is $2.50 per hour, calculate the mean and standard deviation of the amount of revenue each car generates.

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7.

(a) What are the mean and standard deviation of the average number of moths x⎯⎯⎯x¯ in 65 traps?
(b) Use the central limit theorem to find the probability that the average number of moths in 65 traps is greater than 0.4.

Suppose a coin is tossed 100 times and the number of heads are recorded. We want to test whether the coin is fair. Again, a coin is called fair if there is a fifty-fifty chance that the outcome is a head or a tail. We reject the null hypothesis if the number of heads is larger than 55 or smaller than 45.

Write your H_0 and H_A in terms of the probability of heads, say p.

Find the Type I error rate if the null hypothesis is true.

Calculate the power of the test if the true chance of head is 0.4

Find the p-value if the observed number of heads is 65.

Internet Case 12.7 – Analyzing Stockholders’ Equity and EPS

(MUST POST FIRST) Initial Post – As an employee, write an internal memo to your manager addressing the following:

Using the Internet, locate the most recent annual report of a company of your choosing and write an initial post by responding to the following:

Do not research the company listed in the text.

For the most recent day indicated, what were the highest and lowest prices at which the company’s common stock sold?

Find the company’s balance sheet and determine the following: the number of outstanding shares of common stock and the average price at which those shares were originally sold.

What is the relationship between the current market price and the amount you have calculated in part b as the average price at which the stock originally sold?

Find the company’s income statement and identify the trend in basic earnings per share, including discontinued operations. Did discontinued operations have a significant impact on EPS?

For the most recent year, what is the average number of shares of common stock that was used to compute basic earnings per share? Why is that number different from the number outstanding in the company’s balance sheet?

Please, no handwritten answers/photo answers. Thank you.