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# Probability

### Solving a Binomial Distribution Problem

Bill must sell three more cars this month to meet his quota. Tonight he has after-dinner appointments with five prospective customers, each of whom happens to be interested in a different car. If he has a %30 chance of success with each customer, what is the probability that he'll meet his quota by tomorrow morning? Suppose that

### Probability, portfolio return, economy risk, mean life, simple price index

See attached file. The following table contains information on the 2002 resident population of the U.S., by age. (Source: The New York Times Almanac 2004, page 277.) Age (years) < 18 18 - 24 25 - 44 45 - 64 â?¥ 65 No. in 000s 1,107,108 452,196 1,270,41 1,068,2

### Random Variables to Measure Level of Interest in a New Product

A company is conducting a survey of 235 people to measure the level of interest in a new product. Assume that the probability of a randomly selected person's being "very interested" is 0.88 and that people are selected independently of one another. a. Find the standard deviation of the percentage who will be found by the surv

### Probability: Problems and Solutions

1. A cooler contains 100 cans of soda covered by ice. There are 30 cans of cola, 40 cans of orange soda, 10 cans of ginger ale, and 20 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected will be cola or orange. 2. Brain

### Decision Tree Analysis

Tech is playing state in the last conference game of the season. Tech is trailing state 21 to 14, with 7 seconds left in the game, when Tech scores a touchdown. Still trailing 21 to 20, tech can either go for 2 points and win or go for 1 point to send the game into overtime. The conference championship will be determined by t

### Decision payoff table for sale of Christmas greeting cards.

6. The manager of the greeting card section of Mazey's department store is considering her order for a particular line of Christmas Cards. The cost of each box of cards is 3.00; each box will be sold for 5.00 during the Christmas season. After Christmas, the cards will be sold for 2.00 a box. The card section manager believe

### Decision Analysis

Miramar Co. is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes as shown in the following payoff table: Product favorable (0.2) Stable (0.7) Unfavorable (0.1) Widge

### Various Aspects of Decision Analysis

5. A payoff table (profits) is shown below: States of Nature Decisions S1 S2 S3 D1 10 8 6 D2 14 15 2 D3 7 8 9 a. Using the maximax criterion, what decision should be made by the decision maker? b. Using the maximin criterion, what decision should be made by the decision maker? c. Using an equal likel

### Probability: Binomial and Normal Distribution

3. A new county hospital is attempting to determine whether it needs to add a particular specialist to its staff. Five percent of the general hospital population in the county contracts the illness the specialist would treat. If 12 patients check into the hospital in a day, what is the probability that 4 or more will have the i

### Statistics Simulation Problems: Hoylake Rescue Squad, Petroco Service Station

The Hoylake Rescue Squad receives an emergency call every 1,2,3,4,5, or 6 hours according to the following probability distribution. The squad is on duty 24 hrs per day, 7 days ... 2. The time between arrivals of cars at the Petroco Service Station is defined by the following probability distribution ... 3. The Dynaco Manufac

### Statistics: Construct a binomial distribution for habits of other drivers

The graph below shows the results of a survey of drivers who were asked to name the most annoying habit of other drivers. You randomly select six people who participated in the survey and ask each one of them to name the most annoying habit of other drivers. Let x represent the number who named talking on cell phones as the most

### Statistics: Probability of Die Rolls

A 6-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in a 1 a ball is drawn from box A, if the roll results in a 2 or a 3 a ball is drawn from box B, and if the roll results in a 4, 5, or 6 a ball is drawn from box C. If box A contains 1 red, 6 white, and 3 black

### Probability, Binomial Theorem and Z-Score

1. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces: Exactly 5 will be defective? 5 o

### Statistics

The average monthly gasoline purchase for a family with 2 cars is 90 gallons. This statistic has a normal distribution with a standard deviation of 10 gallons. A family is chosen at random. (a) Find the probability that the family's monthly gaoline purchases will be between 88 and 98 gallons. (b) Find the probability that the

### Determining Probability: Scholarship Example

Scores on an assessment exam at a private school are normally distributed, with a mean of 72 and a standard deviation of 8. Any student who scores in the top 5% is eligible for a scholarship. What is the lowest whole number score you can earn and still be eligible for a scholarship?

### Probability: Length of Time to Complete a Cable Installation

See attached file. Q5 The length of time to do a cable installation by a cable company is normally distributed with a mean of 43.2 minutes and a standard deviation of 5.5 minutes. Refer to the megastat output ub Table 5B attached. a) If the cable company wants to establish a standard cable installation appointment time to

### Statistics: What is the length of time for a full service oil change; standard deviation

See attached file. The length of time to complete a a full service oil change is normally distributed with a mean of 15.8 minutes with a standard deviation of 2.2 minutes. Refer to table 4A megastat output attached. A) Analyze the output determine what percentage complete full oil change will fall between 15 and 21 min

### Calculating probability based on binomial distribution.

See attached file. The probability of obtaining a home equity loan from United Bank is 0.40. A random sample of 10 applications was selected. Find the probability that at least five will get a loan. Use the attached binomial probability distribution table 3A

### Probability: Insurance Company & Geographical Region

See Table 2C attached. The table gives a number of claims at a large insurance company by kind of geographical region. East South Midwest West Totals Hospitalization 102 98 39 62 301 Physician's Visit 263 514 120 351 1248 Outpatient Treatment 100 226 65 99 490 Totals 465 838 224 512 2039 A) Referring to the table,

### Probability of meeting someone from Accounting Department

You have just been hired by the JFC Engineering Company. It is a mid-size company located in Phoenix, Arizona. Your prior experience has been with very small firms of less than ten employees, so you are excited about the opportunity of working for a much larger firm. You want to make sure and get to know as many of the employees

### Research and Evaluation: Chapter 5 Exercises 5.62 and 5.70

Chapter 5 - Chapter Exercises 5.62 and 5.70 Note: Methods of computation could include the usage of Excel®, SPSS®, Lotus®, SAS®, MINITAB®, or by hand computation. 5.62 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight

### Statistics: Probability tree for large dollar amount orders that are heavy in weight

Your firm has classified orders as either large or small in dollar amount and as either light or heavy in shipping weight. In the recent past, 28% of orders have been large dollar amounts, 13% of orders have been heavy and 10% of orders have been large in dollar amounts and heavy in weight. a. Complete a probability tree for

### Probability of a big order is 0.4; probability of losing money this quarter is 0.5. Assuming that these are mutually exclusive events. Find the probability of getting the order or losing money.

The probability of getting a big order currently under negotiation is 0.4. The probability of losing money this quarter is 0.5. a. Assuming that these are mutually exclusive events. Find the probability of getting the order or losing money. b. Assuming that these are mutually exclusive events.Does this rule out the possibi

### Probability based on uniform distribution.

The scheduled commuting time on the Long Island Rail Road from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What is the probability that the commuting time will be a. less than 70 minutes? b. between 65 and 70 minutes? c. greater than

### Probability

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. (b) Why might a driver be tempted not to use a seat belt "

### Statistics

1. (10 points) The Pizza Company claims they will deliver your in less than 30 minutes. An undercover consumer reporter monitored a random sample of 30 pizza deliveries at a National outlet. The number of minutes to perform the delivery is reported below. 44, 12, 22, 31, 26, 22, 30, 26, 18, 28, 12, 40, 17, 13, 14, 17, 25, 2

### Probability

The ratings for "driving distance off the tee" for the top 10 golfers on the PGA Tour are as follows: RANK PREV RANK PLAYER VALUE (YDS) 1 1 Scott Hend 318.90 2 2 Tiger Woods 315.20 3 3 Brett Wetterich 310.70 4 4 John Daly 308.50 5 6 Scott Gutschewski 308.40 6 5 Hank Kuehne 308.30 7 10 Davis Love III 304.30 How wou

### Random Variables Factors

The standard error of the sample mean is equal to 5 when n=25. If he sample size increases by a factor of four, how will the standard error change? A random variable follows the student's t distribution. The probability that it will be positive is

### Poisson Distribution with Mean

The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 5.5 tickets per day Interpret the value of the mean. Which of the following cannot generate a Poisson distribution? 1.

### Probability based on binomial distribution.

The information Commons in the main library has 150 personal computers.. The probability that any on the them will require repair on a given day is 0.02. To find the probability that exactly 25 of the computers will require-repair, one would use what type of probability distribution?