Say the fraction of students at college 1 who took statistics is given by 1/5. Say the fraction of students at college 2 who took statistics is given by 1/2. You survey 10 people from each college (so 20 people in total).

(a) What is the probability that more than half of the surveyed students took statistics from college 1?

(b) What is the probability that more than half of the surveyed students took statistics from college 2?

(c) Assuming that the colleges are independent, what is the probability that more than half of the surveyed students took statistics from college 1 and more than half of the surveyed students took statistics from college 2?

(d) Assuming that the colleges are independent, what is the probability that more than half of the surveyed students took statistics from college 1 or more than half of the surveyed students took statistics from college 2?

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Now say you redo your survey of college 1, but you have not decided how many students to ask, so you just keep asking students indefinitely.

(a) What is the probability that none of the first 3 people have taken statistics?

(b) What is the probability that the first person you find who takes statistics is the 5th person you ask?

(c) What is the probability that the first person you find who takes statistics is the 5th person you ask, given that none of the first 3 people have taken statistics?

QUESTION 11

In any given year, one in three Americans over the age of 65 will experience a fall.  If you have three living grandparents over the age of 65, and assuming that the probability of a fall for each grandparent is independent:

What is the probability that none of the three grandparents will experience a fall?  Provide your answer as a decimal between 0 and 1.

4 points   

QUESTION 12

What is the probability that one or more grandparents will experience a fall?  Provide your answer as a decimal between 0 and 1.

4 points   

QUESTION 13

Below are the data (n=100) from a randomized trial designed to evaluate the effectiveness of a newly developed pain reliever designed to reduce pain in patients following joint replacement surgery. The trial compared the new pain reliever to the pain reliever currently in use (called the standard of care).  The outcome of interest was reduction of pain rating (3 or more scale points are considered a clinically meaningful reduction).

What is the probability of experiencing a clinically meaningful reduction in pain given that the patient received the new pain reliever? (express this probability as a decimal between 0 and 1)

4 points   

QUESTION 14

What is the probability that a patient in this trial received the new pain reliever, given that they experienced a clinically meaningful reduction in pain? (express this probability as a decimal between 0 and 1)

A boat capsized and sank in a lake. Based on an assumption of a mean weight of146​lb, the boat was rated to carry 50 passengers​ (so the load limit was 7,300​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 146lb to170lb. Complete parts a and b below.

A) a. Assume that a similar boat is loaded with 50 ​passengers, and assume that the weights of people are normally distributed with a mean of 177.3lb and a standard deviation of 39.4lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 146lb. The probability is

B) b. The boat was later rated to carry only 15 ​passengers, and the load limit was changed to 2,550 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170​(so that their total weight is greater than the maximum capacity of 2,550 ​lb). The probability is

Do the new ratings appear to be safe when the boat is loaded with 15 passengers? Choose the correct answer below.

A. Because there is a high probability of​ overloading, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.

B.Because 177.3 is greater than170 the new ratings do not appear to be safe when the boat is loaded with 15 passengers.

C.Because the probability of overloading is lower with the new ratings than with the old​ ratings, the new ratings appear to be safe.

D.Because there is a high probability of​ overloading, the new ratings appear to be safe when the boat is loaded with 15 passengers.

Core i5 and i7 are two different types of CPU manufactured by Intel. As you may know as a matter of fact, Intel does not produce two types of CPUs. Instead, they just produce Core i7 chips. However, since a chip contains many millions of transistors, some of the transistors may not work properly, while other regions from the chip are working perfectly. In this case, Intel does not scrap the chip to trash, as it will be a waste, but deactivates the malfunctioning region and sell it as a cheaper chip, named Core i5, with less but perfectly functional features. Suppose an assembly line is able to manufacture 3000 chips per day. The probability that a chip meets the Core i7 standard is independently 1/1000. (While the background of this question is real, the probability here is much lower than the true probability.) An assembly line is qualified if it is able to produce at least 3 Core i7 per day. (a) Write down the exact expression of the probability that this assembly line is qualified if it operates only one day. (b) Write down a relevant approximate expression for the probability from (a).

Consider the assembly line described in the above question. Since Core i7 makes much more profit than Core i5, Intel decides to manufacture more chips in a day in order to produce sufficient Core i7 chips per day with high probability. Specifically, the CEO wants to get at least 3 Core i7 chips per day with probability at least 0.999. How many assembly lines should Intel purchase in total?

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 = 72 and estimated standard deviation σ = 41. 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 not normal.The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 20.50.    The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 28.99.The probability distribution of x is approximately normal with μ_x = 72 and σ_x = 41.

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?

YesNo    

You are required to come up with a single header file (IntList.h) that declares and implements the IntNode class (just copy it exactly as it is below) as well as declares the IntList Class interface only. You are also required to come up with a separate implementation file (IntList.cpp) that implements the member functions of the IntList class. While developing your IntList class you must write your own test harness (within a file named main.cpp). Never implement more than 1 or 2 member functions without fulling testing them with your own test harness.

IntNode struct

I am providing the IntNode class you are required to use. Place this class definition within the IntList.h file exactly as is. Make sure you place it above the definition of your IntList class. Notice that you will not code an implementation file for the IntNode class. The IntNode constructor has been defined inline (within the class declaration). Do not write any other functions for the IntNode class. Use as is.

struct IntNode {
    int data;
    IntNode *next;
    IntNode(int data) : data(data), next(0) {}
};

IntList class

Encapsulated (Private) Data Fields

head: IntNode *

tail: IntNode *

Public Interface (Public Member Functions)

IntList(): Initializes an empty list.

~IntList(): Deallocates all remaining dynamically allocated memory (all remaining IntNodes).

void display() const: Displays to a single line all of the int values stored in the list, each separated by a space. This function does NOToutput a newline or space at the end.

void push_front(int value): Inserts a data value (within a new node) at the front end of the list.

void pop_front(): Removes the value (actually removes the node that contains the value) at the front end of the list. Does nothing if the list is already empty.

bool empty() const: Returns true if the list does not store any data values (does not have any nodes), otherwise returns false.

main.cpp test harness for lab

Use this main.cpp file for testing your IntList.

#include <iostream>

using namespace std;

#include "IntList.h"


int main() {

  //tests constructor, destructor, push_front, pop_front, display

   {
      cout << "\nlist1 constructor called";
      IntList list1;
      cout << "\npushfront 10";
      list1.push_front(10);
      cout << "\npushfront 20";
      list1.push_front(20);
      cout << "\npushfront 30";
      list1.push_front(30);
      cout << "\nlist1: ";
      list1.display();
      cout << "\npop";
      list1.pop_front();
      cout << "\nlist1: ";
      list1.display();
      cout << "\npop";
      list1.pop_front();
      cout << "\nlist1: ";
      list1.display();
      cout << "\npop";
      list1.pop_front();
      cout << "\nlist1: ";
      list1.display();
      cout << endl;
   }
   cout << "list1 destructor called" << endl;

   return 0;
}

The returns on the common stock of Cycles, Inc. are quite cyclical. In a boom economy, the stock is expected to return 30 percent in comparison to 12 percent in a normal economy and a negative 20 percent in a recessionary period. The probability of a recession is 30 percent, while the probability of a boom is 5 percent. The probability that the economy will be at normal levels is 65 percent. Assume you have already calculated the Expected Return on this stock as 3.33% or .0333. What is the standard deviation of the return on this stock?

An insurance company has written two life insurance policies for a husband and wife. Policy 1 pays $10,000 to their children if both husband and wife die during this year. Policy 2 pays $100,000 to the surviving spouse if either husband or wife dies during this year. The probability that the husband will die this year is .011. The probability that the wife will die this year is .008. Find the probability that each policy will pay a benefit this year. Assume that the deaths of husband and wife are independent

It is found that 60% of American victims of healthcare fraud are senior citizens. Suppose that I have randomly sampled 100 victims, and I am looking at the count, x, of how many of those victims were senior citizens. Find the following:

a. the mean, variance and standard deviation of the distribution

b. the probability that at least 50 are senior citizens

c. the probability that 75 of them are senior citizens

d. the probability that less than 55 of them are senior citizens

Attendance at large exhibition shows in Denver averages about 7830 people per day, with standard deviation of about 515. Assume that the daily attendance figures follow a normal distribution. (Round your answers to 4 decimal places.)

(a) What is the probability that the daily attendance will be fewer than 7200 people?


(b) What is the probability that the daily attendance will be more than 8900 people?


(c) What is the probability that the daily attendance will be between 7200 and 8900 people?