In a certain game of? chance, a wheel consists of 42 slots numbered? 00, 0,? 1, 2,..., 40. To play the? game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts? (a) through? (c) below. ?(a) Determine the sample space. Choose the correct answer below. A. The sample space is? {00}. B. The sample space is? {00, 0,? 1, 2,..., 40?}. C. The sample space is? {00, 0}. D. The sample space is? {1, 2,..., 40?}. ?(b) Determine the probability that the metal ball falls into the slot marked 7. Interpret this probability. The probability that the metal ball falls into the slot marked 7 is nothing. ?(Round to four decimal places as? needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ?(Type a whole? number.) A. If the wheel is spun 1000? times, it is expected that exactly nothing of those times result in the ball not landing in slot 7. B. If the wheel is spun 1000? times, it is expected that about nothing of those times result in the ball landing in slot 7. ?(c) Determine the probability that the metal ball lands in an odd slot. Interpret this probability. The probability that the metal ball lands in an odd slot is nothing. ?(Round to four decimal places as? needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ?(Type a whole? number.) A. If the wheel is spun 100? times, it is expected that exactly nothing of those times result in the ball not landing on an odd number. B. If the wheel is spun 100? times, it is expected that about nothing of those times result in the ball landing on an odd number.

A.) A piston has an external pressure of 5.00 atm. How much work has been done in joules if the cylinder goes from a volume of 0.170 liters to 0.570 liters?

B.) An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing gas behavior) occurs at a constant pressure of 35.0 atm and releases 73.8 kJ of heat. Before the reaction, the volume of the system was 7.00 L . After the reaction, the volume of the system was 3.00 L .

Calculate the total internal energy change, ΔE, in kilojoules.

C.)

An ideal gas (which is is a hypothetical gas that conforms to the laws governing gas behavior) confined to a container with a massless piston at the top. (Figure 2) A massless wire is attached to the piston. When an external pressure of 2.00 atm is applied to the wire, the gas compresses from 4.40 to 2.20 L . When the external pressure is increased to 2.50 atm, the gas further compresses from 2.20 to 1.76 L .

In a separate experiment with the same initial conditions, a pressure of 2.50 atm was applied to the ideal gas, decreasing its volume from 4.40 to 1.76 L in one step.

If the final temperature was the same for both processes, what is the difference between q for the two-step process and q for the one-step process in joules?

D.) A volume of 120. mL of H2O is initially at room temperature (22.00 ∘C). A chilled steel rod at 2.00 ∘C is placed in the water. If the final temperature of the system is 21.40 ∘C , what is the mass of the steel bar?

Use the following values:

specific heat of water = 4.18 J/(g⋅∘C)

specific heat of steel = 0.452 J/(g⋅∘C)

E.) The specific heat of water is 4.18 J/(g⋅∘C). Calculate the molar heat capacity of water.

1.I recently asked 100 middle school students to complete a statistics test. The mean score on the test was 30 points with a standard deviation of 5 points. The scores followed a normal distributions. Using this information, calculate the following:

a. What is the probability a student earned a score of 45 points or less? P (score < 45 points) =

b. What is the probability a student earned a score higher than 30 points? P(score > 30) =

c. What is the probability a student earned a score between 25 and 45 points? P (25 points < score < 45 points) =

d. I want to know the cutoff value for the upper 10%. What score separates the lower 90% of scores from the upper 10%? P (score < _______) = 90% or 0.90 cumulative area to the left

e. I want to know the cutoff values for the lowest 25%. P (score < ________) = 25% or 0.25 cumulative area to the left

f. I would also like to know the cut off values for the highest 25%. P (score > _______) = 25% or 0.25 cumulative area to the right

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level, the number of points Naomi scores has a Discrete Uniform distribution on [6,12] and the number of points Isaac scores has a Discrete Uniform distribution on [7, 10]. Each time they play, their scores are independent.

(a) (2) Write down an expression for the probability that in 100 games, the total number of points scored by Naomi and Isaac is at least 1800. Do not evaluate the expression.

(b) (2) Find the mean and variance of the total number of points scored by Naomi and Isaac in one game.

(c) (6) Using the Central Limit Theorem, find the approximate probability in (a). You should use a continuity correction. Justify why the approximation is appropriate in this situation.

(d) (5) Suppose Naomi and Isaac want to play until they have a 99% probability of being above a total score of 1800. What is the smallest number of games they must play to achieve this?

Question 1: A drive-in movie theatre charges viewers by the carload but keeps careful records of the number of people in each car. The probability distribution for the number of people in each car entering the drive-in is given in the table. x = (px) 1= 0.02 2= 0.30 3=0.10 4= 0.30 5= 0.20 6=0.08 a. Suppose two cars entering the drive-in are selected at random. Find the exact probability distribution for the maximum number of people in either one of the cars, M. (Show all your work in order to get full marks, i.e., show: 1. the total number of samples of two cars, 2. the list all the possible samples of two cars, the value of max, and the corresponding probability. 3. the exact distribution for the maximum number of people in either one of the cars). b. Find the mean, variance, and standard deviation of M.

Please provide answer with full details!

Diana's kids, Naomi and Isaac, play a lot of video games together. On a particular level, the number of points Naomi scores has a Discrete Uniform distribution on [5,11] and the number of points Isaac scores has a Discrete Uniform distribution on [6, 9]. Each time they play, their scores are independent.

(a) (2) Write down an expression for the probability that in 100 games, the total number of points scored by Naomi and Isaac is at least 1600. Do not evaluate the expression.

(b) (2) Find the mean and variance of the total number of points scored by Naomi and Isaac in one game.

(c) (6) Using the Central Limit Theorem, find the approximate probability in (a). You should use a continuity correction. Justify why the approximation is appropriate in this situation.

(d) (5) Suppose Naomi and Isaac want to play until they have a 96% probability of being above a total score of 1600. What is the smallest number of games they must play to achieve this?

JAVA

* This is a skeleton file. Complete the functions below. You
* may also edit the function "main" to test your code.
*
* You should not use any loops or recursions. Your code needs to run in
* constant time. It is OK if your testing code has loops (like in checkInvariants).
*
* You must not add fields or static variables. As always, you must not change
* the declaration of any method nor the name of the class or of this file.
*/

public class Deque {

   private Node first;   // A reference to the first item in the Dequeue (or
                           // null if empty)
   private Node last;   // A reference to the last item in the Dequeue (or
                           // null if empty)
   private int N;            // The number of items currently in the Dequeue

   static class Node {
      
       public T item;           // The data stored at this node.
       public Node next;   // The node to the right (or null if there is no
                               // node to the right)
       public Node prev;   // The node to the lett (or null if there is no
                               // node to the left)
   }

   /**
   * Construct an empty Deque.
   */
   public Deque() {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Tests if the Dequeue is empty.
   *
   * @return true if this Deque is empty and false
   * otherwise.
   */
   public boolean isEmpty() {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Returns the number of items currently in this Deque.
   *
   * @return the number of items currently in this Deque
   */
   public int size() {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Inserts an item into the front of this Deque.
   *
   * @param item
   * the item to be inserted
   */
   public void pushFront(T item) {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Inserts an item into the back of this Deque.
   *
   * @param item
   * the item to be inserted
   */
   public void pushBack(T item) {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Removes and returns the item at the front of this Deque.
   *
   * @return the item at the front of this Deque.
   * @throws NoSuchElementException if this Deque is empty.
   */
   public T popFront() {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }

   /**
   * Removes and returns the item at the back of this Deque.
   *
   * @return the item at the back this Deque.
   * @throws NoSuchElementException if this Deque is empty.
   */
   public T popBack() {
       // TODO - Replace the line below with a correct solution.
       throw new RuntimeException("Not implemented");
   }
}

1.A three-course meal at a restaurant consists of a choice of one of 5 salads, one of 7 entrees and one of 4 desserts. If a diner chooses each course of her meal randomly, what is the probability that she will choose: a Cobb salad, grilled ribs with corn on the cob, and a slice of boysenberry cobbler.

2. If the letters ACDEINOTU are arranged in order randomly, what is the probability that the arrangement will spell the word "EDUCATION"

3. A phone number(not counting the area code) consists of a sequence of seven digits from 0-9. What is the probability of randomly generating seven digits and getting the phone number of one of the 25 students in a Statistics class ( assume each student has exactly one phone number)

The probability a telesales represenative making a sale on a customer call is .15. Find the probability: 1. Her first sale comes after 5 calls. 2. Her first 5 calls went with out a sale. What is the probability she will have to make no more than 13 calls until her first sale? 3. Less than 2 sales are made on 5 calls Represenatives are required to make an average of at least 4 sales a day or they are fired. 4. Find the least number calls the represenative is required to make a day so not to be fired. 5. Compute the variance for the number sales made in a day if she makes the minimum number of call to keep her job.