A survey showed that 79​% of adults need correction​ (eyeglasses, contacts,​ surgery, etc.) for their eyesight. If 20 adults are randomly​ selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight​ correction? The probability that no more than 1 of the 20 adults require eyesight correction is nothing.

Create MySortedArrayCollection.java

• This file is inherited from SortedArrayCollection.java
• This file implements MySortedArrayCollectionInterface.java

****** Make new and just complete MySortedArrayCollection.java, dont modify others

////////////////////////////////////////////////////////

SortedArrayCollection.java

public class SortedArrayCollection<T> implements CollectionInterface<T> {
   protected final int DEFCAP = 100; // default capacity
   protected int origCap; // original capacity
   protected T[] elements; // array to hold collection elements
   protected int numElements = 0; // number of elements in this collection

   // set by find method
   protected boolean found; // true if target found, otherwise false
   protected int location; // indicates location of target if found,
                           // indicates add index if not found

   public SortedArrayCollection() {
       elements = (T[]) new Object[DEFCAP];
       origCap = DEFCAP;
   }

   public SortedArrayCollection(int capacity) {
       elements = (T[]) new Object[capacity];
       this.origCap = capacity;
   }

   protected void enlarge()
   // Increments the capacity of the collection by an amount
   // equal to the original capacity.
   {
       // Create the larger array.
       T[] larger = (T[]) new Object[elements.length + origCap];

       // Copy the contents from the smaller array into the larger array.
       for (int i = 0; i < numElements; i++) {
           larger[i] = elements[i];
       }

       // Reassign elements reference.
       elements = larger;
   }

   protected void find(T target)
   // Searches elements for an occurrence of an element e such that
   // e.equals(target). If successful, sets instance variables
   // found to true and location to the array index of e. If
   // not successful, sets found to false and location to the
   // array index where target should be inserted.
   {
       location = 0;
       found = false;
       if (!isEmpty())
           recFind(target, 0, numElements - 1);
   }

   protected void recFind(T target, int first, int last)
   // Used by find.
   {
       int result; // result of the comparison
       if (first > last) {
           found = false;
           result = ((Comparable) target).compareTo(elements[location]);
           if (result > 0)
               location++; // adjust location to indicate insert index
       } else {
           location = (first + last) / 2;
           result = ((Comparable) target).compareTo(elements[location]);
           if (result == 0) // found target
               found = true;
           else if (result > 0) // target too high
               recFind(target, location + 1, last);
           else // target too low
               recFind(target, first, location - 1);
       }
   }

   public boolean add(T element)
   // Precondition: element is Comparable to previously added objects
   //
   // Adds element to this collection.
   {
       if (numElements == elements.length)
           enlarge();

       find(element); // sets location to index where element belongs

       for (int index = numElements; index > location; index--)
           elements[index] = elements[index - 1];

       elements[location] = element;
       numElements++;
       return true;
   }

   public boolean remove(T target)
   // Removes an element e from this collection such that e.equals(target)
   // and returns true; if no such element exists, returns false.
   {
       find(target);
       if (found) {
           for (int i = location; i <= numElements - 2; i++)
               elements[i] = elements[i + 1];
           elements[numElements - 1] = null;
           numElements--;
       }
       return found;
   }

   public int size()
   // Returns the number of elements on this collection.
   {
       return numElements;
   }

   public boolean contains(T target)
   // Returns true if this collection contains an element e such that
   // e.equals(target); otherwise, returns false.
   {
       find(target);
       return found;
   }

   public T get(T target)
   // Returns an element e from this collection such that e.equals(target);
   // if no such element exists, returns null.
   {
       find(target);
       if (found)
           return elements[location];
       else
           return null;
   }

   public boolean isEmpty()
   // Returns true if this collection is empty; otherwise, returns false.
   {
       return (numElements == 0);
   }

   public boolean isFull()
   // This collection is unbounded so always returns false.
   {
       return false;
   }
}
///////////////////////////////////////////////////////

MySortedArrayCollectionInterface.java

public interface MySortedArrayCollectionInterface<T> extends CollectionInterface<T> {
   public String toString();
   // Creates and returns a string that correctly represents the current
   // collection.
   // Such a method could prove useful for testing and debugging the class and for
   // testing and debugging applications that use the class.
   // Assume each stored element already provides its own reasonable toString
   // method.

   public T smallest();
   // Returns null if the collection is empty, otherwise returns the smallest
   // element of the collection.

   public int greater(T element);
   // Returns a count of the number of elements e in the collection that are
   // greater then element, that is such that e.compareTo(element) is > 0

   public MySortedArrayCollection<T> combine(MySortedArrayCollection<T> other);
   // Creates and returns a new SortedArrayCollection object that is a combination
   // of this object and the argument object.

   public T[] toArray();
   // Returns an array containing all of the elements of the collection.

   public void clear();
   // Removes all elements.

   public boolean equals(Object o);
   // Takes an Object argument, returning true if it is equal to the current
   // collection and false otherwise

   public boolean addAll(MySortedArrayCollection<T> c);
   // Takes a MySortedArrayCollection argument and adds its contents to the current
   // collection;
   // returns a boolean indicating success or failure.

   public boolean retainAll(MySortedArrayCollection<T> c);
   // Takes a MySortedArrayCollection argument and removes any elements from the
   // current collection that are not in the argument collection; returns a boolean
   // indicating success or failure.

   public void removeAll(MySortedArrayCollection<T> c);
   // Takes a MySortedArrayCollection argument and removes any elements from the
   // current collection that are also in the argument collection.
}

//////////////////////////////////////////////

CollectionInterface.java

public interface CollectionInterface<T> {
   boolean add(T element);
   // Attempts to add element to this collection.
   // Returns true if successful, false otherwise.

   T get(T target);
   // Returns an element e from this collection such that e.equals(target).
   // If no such e exists, returns null.

   boolean contains(T target);
   // Returns true if this collection contains an element e such that
   // e.equals(target); otherwise returns false.

   boolean remove(T target);
   // Removes an element e from this collection such that e.equals(target)
   // and returns true. If no such e exists, returns false.

   boolean isFull();
   // Returns true if this collection is full; otherwise, returns false.

   boolean isEmpty();
   // Returns true if this collection is empty; otherwise, returns false.

   int size();
   // Returns the number of elements in this collection.
}

Snow White recieves a basket of 11 apples, out of which 2 of them are poisoned. She decides to eat 4 of them. Let X1 denote the number of unpoisoned apples that she eats.
Check all that are true about X1.
A. We can model X1 with a collection of trials
B. The trials are independent
C. The trials have two outcomes
D. The trials have the same probability of success.
E. There are a set number of trials

Snow White recieves an unlimited basket of apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She makes the questionable choice to keep eating them until she eats a poisoned one. Let X2 denote the number of unpoisoned apples that she eats.
Check all that are true about X2.
A. The trials have two outcomes
B. We can model X2 with a collection of trials
C. There are a set number of trials
D. The trials are independent
E. The trials have the same probability of success.

Snow White recieves a basket of 4 apples, all of whom are either poisoned or not. There is a 0.4 chance they are poisoned. She decides to eat all of them. Let X3 denote the number of unpoisoned apples that she eats.
Check all that are true about X3.
A. The trials have the same probability of success.
B. There are a set number of trials
C. The trials are independent
D. We can model X3 with a collection of trials
E. The trials have two outcomes

Snow White recieves a basket of 4 apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She decides to eat all of them. Let X4 denote the number of unpoisoned apples that she eats.
Check all that are true about X4.
A. The trials are independent
B. We can model X4 with a collection of trials
C. The trials have two outcomes
D. There are a set number of trials
E. The trials have the same probability of success.

Which of the following are a binomial random variable?
A. X1
B. X2
C. X4
D. X3

Snow White recieves a basket of 11 apples, out of which 3 of them are poisoned. She decides to eat 5 of them. Let X1denote the number of unpoisoned apples that she eats.
Check all that are true about X1.
A. The trials are independent
B. The trials have two outcomes
C. The trials have the same probability of success.
D. There are a set number of trials
E. We can model X1 with a collection of trials

Snow White recieves an unlimited basket of apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She makes the questionable choice to keep eating them until she eats a poisoned one. Let X2 denote the number of unpoisoned apples that she eats.
Check all that are true about X2.
A. The trials have two outcomes
B. We can model X2 with a collection of trials
C. The trials have the same probability of success.
D. The trials are independent
E. There are a set number of trials

Snow White recieves a basket of 5 apples, all of whom are either poisoned or not. There is a 0.4 chance they are poisoned. She decides to eat all of them. Let X3 denote the number of unpoisoned apples that she eats.
Check all that are true about X3.
A. The trials have two outcomes
B. There are a set number of trials
C. We can model X3 with a collection of trials
D. The trials have the same probability of success.
E. The trials are independent

Snow White recieves a basket of 5 apples, each of which has a 0.4 chance of being poisoned, regardless of the status of other apples. She decides to eat all of them. Let X4 denote the number of unpoisoned apples that she eats.
Check all that are true about X4.
A. The trials are independent
B. We can model X4 with a collection of trials
C. The trials have the same probability of success.
D. There are a set number of trials
E. The trials have two outcomes

Which of the following are a binomial random variable?
A. X2
B. X4
C. X3
D. X1

Do a hypothesis for the following, make sure to include and label all five steps:

    Test the claim that the proportion of wins is the same whether the wear a shirt

    and tie or jeans and a t-shirt. Use a .05 significance level.

An urn contains 5000 balls, of which 100 are yellow and the remaining are purple. We draw 20 balls from the urn and denote the number of yellow balls drawn by X.

(a) What kind of random variable is X if the draws are performed without replacement? Write down the probability distribution function f(x) of X and compute P(X = 5).
(Give an exact expression for the probability that is asked but do not evaluate!)

(b) What kind of random variable is X if the draws are performed with replacement? Write down the probability distribution function f(x) of X and compute P(X ≤ 2). (Give an exact expression for the probability that is asked but do not evaluate!)

(c) Use Poisson distribution to approximate the probability asked in part (b).

A subway train on the Red Line arrives every 8 minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

A. Enter an exact number as an integer, fraction, or decimal.
μ =

B.  σ = Round your answer to two decimal places.

C. Find the probability that the commuter waits less than one minute.

D. Find the probability that the commuter waits between five and six minutes.

E. State "80% of commuters wait more than how long for the train?" in a probability question. (Enter your answer to one decimal place.)
Find the probability that the commuter waits more than __ minutes. Draw the picture and find the probability.

1. ****NEED TO KNOW HOW PROBLEM IS SET UP IN EXCEL***
2. During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.
   1. Clearly state what the random variable in this problem is?
   2. What is an appropriate distribution to be used for this problem and why?
   3. What is the expected number of calls in one hour?
   4. What is the probability of receiving three calls in five minutes?
   5. What is the probability of receiving NO calls in a 10-minute period?
   6. What is the probability of receiving more than five calls in a 10-minute period?
   7. What is the probability of receiving less than seven calls in 15-minutes?
   8. What is the probability of receiving at least three but no more than 10 calls in 12 minutes?

A Carnot heat engine receives heat at 850 K and rejects the waste heat to the environment at 298 K.
The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat
from the cooled space at -17⁰C at a rate of 450 kJ/min and rejects it to the same environment at 298
K. Determine;
(a) the rate of heat supplied to the heat engine and
(b) the total rate of heat rejection to the environment.

an air-conditioner on a hot summer day removes 8 kW of energy at 21°C and pushes energy to the outside which is 31°C. the house has 15000 mg mass with an average specific heat of .95 kJ/mg K. in order to do this, the cold side of the air-conditioner is at 5°C and the hot side is at 40°C the air-conditioner COP of 60%. Find the power to run the air-conditioner