Micromedia, venture capital, widget defect, job data

13.
Micromedia offers computer training seminar on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting, Micromedia is currently planning a two -day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $300 per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $4800. Micromedia rent computers for its seminars at a cost of $30 per computer per day.
a) Develop a model for the total cost to put on the seminar. Let x represent the number of students who enroll in the seminar.
b) Develop a model for the total profit if x students enrolls in the seminar.
c) Micromedia have forecasted an enrollment of 30 students for the seminar. How much profit will be earned if their forecast is accurate?
d) Compute the breakeven point.

Chapter 2
4
The availability of venture capital provided a big boost in funds available to companies in recent years. According to Venture Economics (Investor's Business Daily, April 28, 2000), 2374 venture capital disbursement were made in 1999. Of these, 1434 were to companies in California, 390 were to companies in Colorado. Twenty-two percent of the companies in New York, and 112 were to companies in Massachusetts, 217 were companies receiving funds were in the early stages of development and 55% of the companies were in an expansion stage. Suppose you want to randomly choose one of these companies to learn about how they used the funds.
a) What is the probability the company chosen will be from California?
b) What is the probability the company chosen will not be from one of the four states mentioned?
c) What is the probability the company will not be in the early stages of development?
d) Assuming the companies in the early stages of development were evenly distributed across the country, how many Massachusetts companies receiving venture capital funds were in the early stages of development?
e) The total amount of funds invested was $ 32.4 billion. Estimated the amount that went to Colorado.

10
A quality control specialist has sampled 25 widgets from the production line. A widget can have minor or major defects. On the sampled widgets, 4 have minor defects and 2 have major defects. What is the probability that a widget has a major defect, given that it has a defect?

17
A study of job satisfaction was conducted for four occupations: cabinetmaker, lawyer, physical therapist, and systems analyst. Job satisfaction was measured on a scale of 0-100. The data obtained are summarized in the following cross-tabulation.

Occupation Under 50 50-59 60-69 70-79 80-89
Cabinetmaker 0 2 4 3 1
Lawyer 6 2 1 1 0
Physical Therapist 0 5 2 1 2
Systems Analyst 2 1 4 3 0

a) Develop a joint probability table.
b) What is the probability a randomly chosen participant has a satisfaction score in the 80s?
c) What is the probability of a satisfaction score in the 80s given the study participant was a physical therapist?
d) What is the probability a randomly chosen participant is a lawyer?
e) What is the probability a randomly chosen participant is a lawyer and received a score under 50?
f) What is the probability of a satisfaction score under 50 given a person is a lawyer?
g) What is the probability of a satisfaction score of 70 or higher?

23
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P(high-quality oil)=0.50
P(medium-quality oil)=0.20
P(no oil)=0.30
a) What is the probability of finding oil?
b) After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are
P(soil / high-quality oil)= 0.20
P(soil/ medium-quality oil) = 0.20
P(soil/ no oil)= 0.30
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?

Chapter 3
4
Shown is a probability distribution for the random variable x
X f(x)
3 0.25
6 0.50
9 0.25
_________
1.00
a) Compute E(x), the expected value of x.
b) Compute σ² the variance of x.
c) Compute, the standard deviation of x.

11
Harris Interactive survey for InterContinental Hotels & Resorts asked respondent "when traveling internationally, do you generally venture out on your own to experience culture or stick with your tour group and itineraries?" The survey found that 23% f the respondents stick with their tour group (USA today, January 21, 2004).
a) In a sample of six international travelers, what is the probability that two will stick with their tour group?
b) In a sample of six international travelers, what is the probability that at least two will stick with their tour group?
c) In a sample of 10 international travelers, what is the probability that none will stick with the tour group?

14
Consider a Poisson probability distribution with 2 as the average number of occurrences per time period.
a) Write the appropriate Poisson probability function
b) What is the average number of occurrences in three time periods?
c) Write the appropriate Poisson probability function to determine the probability of x occurrences in three time periods.
d) Find the probability of 2 occurrences in one time period.
e) Find the probability of 6 occurrences in three time periods.
f) Find the probability of 5 occurrences in two time periods.

24
The demand for a new product is estimated to be normally distributed with µ = 200 and σ = 40. Let x be the number of units demanded and find the following probabilities:
a) P( 180≤x ≤220)
b) P(x≥250)
c) P(x≤100)
d) P(225≤x≤250)

25
The average stock price for companies making up the S&P 500 is $30, and the standard deviations is $8.20 (Business Week, Special Annual Issue, Spring 2003) Assume the stock prices are normally distributed.
a) What is the probability a company will have a stock price of at least $40?
b) What is the probability a company will have a stock price no higher than $20?
c) How high does a stock price have to be to put a company in the top 10%?

32
The lifetime (hours) of an electronic device is a random variable with the exponential probability density function:
F(x) = 1/50e ̄x/50 for x≥0
a) What is the mean life of the device?
b) What is the probability the device fail in the first 25 hours of operation?
c) What is the probability the devices operate 100 more hours before failure?