#### A Discussion On Probability Distributions

6. A coin is tossed 4 times. Let X denote the number of heads which appear in 4 tosses. a) Construct a probability distribution for X b) Find P(X>2) c) Find the expected value of X d) Find the variance and standard deviation of X 7. The probability that a randomly selected elementary or secon...

#### The solution gives detailed discussion on definitions and calculations of specificity and sensitivity. Some further topics such as positive predictive value, negative predictive value, Lead time bias and length-bias are also explained. All formula of specificity and sensitivity are shown and explained with specific examples.

1) Sensitivity is: A. The probability that a test correctly classifies as positive those who have preclinical disease. B. The probability that a test correctly classifies individuals without preclinical disease as negative C. The probability that those who test positive have the preclinical dise...

#### Probability of Outcome

A fair die is rolled two times. Let A be the event that the outcome of the first roll is an odd number. Let B be the event that the outcome of second roll is at least 5. A) What is the probability that the outcome of the second roll is at least 5, given that the first roll is an odd number? B) ...

#### Probability of a Suspect

The police are looking for a man who wears size 12 shoes and drives a black car. They estimate that 1 in 10 men wears size 12 shoes, and that 1 in 8 men drives a black car. If one man is chosen at random, what is the probability that he matches the description.

#### Probability Of Required University Score

A prestigious university requires a score of at least 750 on a graduate exam for admission to its MBA program. Suppose the graduate exam is normally distributed with a mean of 500 and a standard deviation of 200. If a test taker is randomly selected, what is the probability he or she scores 750 or...

#### Production under normally distributed process

A production process manufactures items with weights that are normally distributed with mean 16 pounds and standard deviation 0.15 pound. An item is considered to be defective if its weight is less than 15.8 pounds or greater than 16.2 pounds. Suppose that these items are currently produced in ba...

#### Developing Decision Trees and Payoffs

How to develop a decision tree and the payoffs using the information given The Problem: Joe Morgan, an investment strategist has learned of a couple alternatives that his company can invest in. His firm has chosen to invest in real estate. Occasionally the firm will invest in commercial real e...

#### Binomial and Poisson Probability Distributions

Suppose you, as the manager of Tennessee Grilled Pork. would like to ensure you have enough cleaning staff for your dining room and would like to analyze data for customers who enter the restaurant to place and order and either eat in the restaurant or take their order to- go. If the probability tha...

#### Probability: Random Sampling

Sample question: A study of the effect of college education on job satisfaction was conducted. A contingency table is presented below: Satisfied with job Not satisfied with job Total Attended College 325 190 515 Did not Attend 186 369 555 Total 511 559 1070 ...

#### The probability associated with clothing orders

1. Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is \$20 while the anticipated selling price is \$50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that dem...

#### Probability Distributions For Continuous Variables

A large company is planning to launch a new product in the market. However, the company is not sure about the state of the economy and its impact on the return on the capital investment associated with this new product. A key analysis in this regard is the expected return and risk. Since the new pro...

#### Statistical Analysis: Annual Return

1. Suppose the annual return on XYZ stock follows a normal distribution with mean 0.12 and standard deviation 0.30. a. What is the probability that XYZ's value will decrease during a year? b. What is the probability that the return on XYZ during a year will be at least 20%? c. What is the ...

#### Calculating the Probability in Random Samples

#25. Companies often make flextime scheduling available to help recruit and keep women employees who have children. Other workers sometimes view these flextime schedules as unfair. An article in USA Today indicates that 25% of male employees state they have to pick u the slack for moms working fle...

#### Using Probability in Court Trials

1. In 1972, Rodrigo Partida, a Mexican-American, was convicted of burglary with intent to commit rape. His conviction took place in Hidalgo County, which is in Texas on the border with Mexico. In Hidalgo County, 79.1% of the residents eligible for jury selection are Mexican-American. Partida's convi...

#### Bayers Theorem

Choose any medical scientific study who applied a Bayer Theorem and write down the article information (title, author, location, and date) of the article, write a paragraph about the summary or overview of the article (You can copy from the article), and write your opinion about the article.

#### The failure of the Space Shuttle Challenger

The January 1986 mission of the Space Shuttle Challenger was the 25th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure. (a) According to NASA, the probability of such a failure in a single mission was 1/ 63,000. Using this value of p and assuming all...

#### Sample Space & Probability

The manager of a small business receives a shipment of five hard drives. Three hard drives are good and 2 are defective. If a computer repair shop purchases 3 of these stock of hard drives from the small business and the selection was made at random: 1. List the elements of the sample space S u...

#### Site Preference for Restaurants

Suppose you manage Tennessee Grilled Pork, a fast food restaurant specializing in pork sandwiches and pork chops on a stick. You have decided to build a new restaurant and have 2 possible site locations (Site 1 and Site 2). Three groups of people make independent recommendations on site preference: ...

#### Probability Relationships

Suppose you, as manager of Tennessee Grilled Pork, will submit proposals for a small business loan and a city business grant to help fund the building of the new location you submitted to the management teams. The probability of acquiring the small business loan is .79 and the probability of obtaini...

#### Statistical Analysis: Probability

1. Find the percentage of the total area under the standard normal curve between the given z-scores. a) Z=.64 and z =2.11 b) Z= -1.63 and z = -1.08 c) Z= - 2.91 and z = -.51 2. Find a z -score satisfying each of the given conditions a) 1% of the total area is to the left Z b) 25% o...

#### Determining Employee Expenditure Using Probability

If you are asked to calculate the probability that a randomly selected employee's expenditure is exactly \$5, what will be your answer? Why? Will your answer be the same for any individual expenditure? Assume that population of all employee expenditures follow a normal distribution. Could you set...