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# Probability

### Two Probability Questions.

1. A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 20%. She also believes that if the economy enters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession the probability that the mutual fund will increase

### Sample size, Sampling distribution of proportions

25) Money magazine reported that the average price of gallon of gasoline in the United States during the first quarter of 2001 was \$ 1.46. Assume the price reported by Money is the population mean, and the population standard deviation is \$ 0.15. a) What is the probability that the mean price for a sample of 30 gas sta

### Probability and mean / standard deviation at electronics firm

The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed with mean = 35 minutes and standard deviation = 6 minutes. Nine first interviews are usually scheduled p

### Probability in birth weight between babies

Consider babies born in the "normal" range of 37 - 43 weeks gestational age. Extensive data supports the assumption that for such babies born in the United States, birth weight is normally distributed with mean = 3432 grams and standard deviation = 482 grams. What is the probability that the birth weight of a randomly selecte

### What is the probability distribution for a radio station that plays music

A radio station that plays classical music has a "By Request" program each Saturday night. The percentage of requests for composers on a particular night are listed below: Composers Percentage of Requests Bach 5 Beethoven 26 Brahms 9 Dvorak 2 Mendelssohn 3 Mozart

### Probability

Let X be a normally distributed random variable with µ = 100 and &#963; = 10. The probability that X is between 70 and 110 is (to the nearest whole percent) a. 8 % b. 84 % c. 95% d. answer not listed

### Acme Airlines - Probability that 12 or fewer passengers holding reservations will actually show up for the flight

Acme Airlines flies airplanes that seat 12 passengers. From experience, they have learned that, on average, 80% of the passengers holding reservations for a particular flight actually show up for the flight. If they book 13 passengers for a flight, what is the probability that 12 or fewer passengers holding reservations will act

### Probability of selecting marbles without replacement

A jar contains 12 marbles, 5 of which are blue and 7 of which are red. If 4 marbles are chosen at random and without replacement, what is the probability of selecting 3 blue ones and 1 red one? a. 5C3 x 7C1/12C4 b. 5P3 x 7P1/12P4 c. 5C2 x 7P2/12 d. Answer not listed

### What is the probability a delivery truck driver will visit the cities on his route in alphabetical order?

A delivery truck must make stops in eight different cities, designated by the first letter in the name of the city: A, B, C, D, E, F, G, and H. If the order in which the truck visits the eight locations is chosen randomly, what is the probability that it will visit them in alphabetical order? a. 8C1/8P1 b. 1/8P8

### Probability

In a survey on the quality of customer service at Car Toys, customers were asked to rate the service on a scale from 1 to 10, with 10 being that a customer was completely satisfied. Assume that the distribution of the responses can be approximated by a normal distribution with a mean of 7 and a std deviation of 1. a. What is

See attached. Review Questions (9, 10 and 15) #'s 9 & 10 refer to the following situation. Fifteen (15) companies all bid on oil leases. The following data is a small part of the records on past bids. All monetary amounts are in millions of dollars. Leases Signals Proven Value Company 1 Company 2 \$105.5 \$99.5 \$107.4

### Probability, Linear Programming

Please see attachment. 1. Roger's Regalia is a manufacturer of caps, gowns, and assorted party outfits, primarily for the commencement season. (80 percent of their yearly sales occur over a six-week period.) One of their popular products is a Parrot Head, sometimes worn by graduating college students as a sign of festive oc

### Probability and Probability Distributions

1) In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults)who have a college degree. Find the variance for the probability distribution. x P(x) 0 0.0256 1 0.1536 2 0.3456 3 0.3456 4 0.1296 2) A

### Small bag of Skittles candies has the following assortment

A small bag of Skittles candies has the following assortment: red (10), blue (2), orange (5), brown (21), green (0), and yellow (18). Construct the probability distribution for x. Total number of candies = 10 + 2 + 5 + 21 + 0 + 18 = 56 P(R) the probability of randomly choosing a red candy. P(B) the probability of rando

### You are trying to set up a portfolio that consists of a corporate bond fund and a common stock fund. Compute the covariance of the corporate bond fund and the common stock fund. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in a corporate bond fund: a. 30% , b. 50%, c. 70%

You are trying to set up a portfolio that consists of a corporate bond fund and a common stock fund. the following information about the annual return (per \$1,000)of each of these investments under different economic condition is available, along with probability that each of these economic conditions will occur: probability

### weights of catfish are normally distributed

1. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds? a) 84% b) 67% c) 29% d) 16% 2. The standard error of t

### Probability and normal distribution : key information

1. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean? a) 0.029 b) 0.050 c) 0.091 d) 0.120 2. The owner of a fish

### Given the following table of payoffs use sensitivity analysis to determine at what probability or more you would select decision 3.

Given the following table of payoffs use sensitivity analysis to determine at what probability or more you would select decision 3. s1 s2 d1 8 10 d2 2 15 d3 10 3 a none of the choices are correct b .5798 c .5454

### At a university with 1000 business majors, 20% are enrolled in a statistics course.

At a university with 1000 business majors, 20% are enrolled in a statistics course. Of these 200 students enrolled in the statistics course, 25% are also enrolled in an accounting course. There are 250 students who are enrolled in accounting and not enrolled in statistics. Of the students is enrolled in statistics, what is the p

### A certain airplane has two independent alternators to provide electrical power.

Prepare answers to the following assignments from the e-text, Applied Statistics in Business and Economics, by Doane and Seward: 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 tw

### Probability: fax costs

Please help me with the attached questions. Please also provide the formulas used and how the numbers are plugged into the formula. Thank you. 1.) Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the averag

### Binomial Tree for Currency Put Option

An American put option to sell a swiss franc for dollars has a strike price of \$0.80 and a time to maturity of one year. The volatility of the swiss franc is 10%, the dollar interest rate is 6%, the swiss franc interest rate is 3%, and the current exchange rate is 0.81. Use a tree with three time steps to value the option. Estim

### The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers.

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker? a. 1/4 b. 1/8 c. 5/8 d. 2/5

### Monte Carlo Simulation

Please see that attached files. Must be completed in Excel (version no higher that 2003). The Excel spreadsheet contains the sample of how the problem should be work (the WORD document is the problem).

### Marginal and Joint Probability

1. A company markets two products (Product A and Product B) through mail order. The company will market them in sequence with the first mail order offer for product A. It feels that there is a 30% chance that any customer will purchase product A. Product B is offered some months later. It is felt, for product B, that there is

### Mary and John toss a coin three times

Mary Tosses a coin 3 times and john does the same. A) Find probability Mary obtains one head. I have that answer which i think is 1/33 or 33%, but do I include John's tosses also in that? b) Find the probability that Mary obtains exactly one head and so does John. Here I thought to do 1/2 times 1/2 = 1/4 is that right?

### The Stripes C-store chain reports that 7% of its credit card holders will default within 5 years.

The Stripes C-store chain reports that 7% of its credit card holders will default within 5 years. It just mailed out 12 new cards today. a.How many of these new cardholders would be expected to default within 5 years? What is the standard deviation? b.What is the likelihood that none of these cardholders will default? c.Wha

### Questions on Binomial Probability

My son plays for the Hooks and his average is .333. Therefore I am going to assume the probability of him getting a hit is .333 for each time he bats. In a recent game he batted three times. What was the probability of him getting at least one hit? What was the probability of him getting two hits in the game? What was the

### Probability: Insurance, Population, Medicare and TV Viewing

1. National Association of Insurance Commissioners The average annual cost of automobile insurance is \$687 (National Association of Insurance Commissioners, January 2003). Use this value as the population mean and assume that the population standard deviation is &#963; = \$230. Consider a sample of 45 automobile insurance polic