3) If you have a 40% probability of winning at a game of roulette, how many games can you expect to win after playing 30 games?
4) Calculate the variance of the problem above.
5) If Sarah rolls a 6-sided number cube, how many times can she expect to roll a 4 if she plays 18 games?
In: Advanced Math
Problem 13-09 (Algorithmic)
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
| Demand for Service | ||
| Service | Strong | Weak |
| Full price | $1380 | -$580 |
| Discount | $980 | $460 |
| Optimistic approach | Full price service |
| Conservative approach | Discount service |
| Minimax regret approach | Discount service |
In: Operations Management
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
| Demand for Service | ||
| Service | Strong | Weak |
| Full price | $1440 | -$530 |
| Discount | $1050 | $480 |
| Optimistic approach | Full price service |
| Conservative approach | Discount service |
| Minimax regret approach | Discount service |
In: Operations Management
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
| Demand for Service | ||
| Service | Strong | Weak |
| Full price | $1440 | -$530 |
| Discount | $1000 | $480 |
| Optimistic approach | |
| Conservative approach | |
| Minimax regret approach |
In: Operations Management
Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full-price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle Beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):
| Demand for Service | ||
| Service | Strong | Weak |
| Full price | $1380 | -$650 |
| Discount | $1000 | $460 |
| Optimistic approach | Full price service |
| Conservative approach | Discount service |
| Minimax regret approach | Discount service |
In: Operations Management
1.) A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 29.8 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 29.8 weeks and that the population standard deviation is 5.9 weeks. Suppose you would like to select a random sample of 194 unemployed individuals for a follow-up study.
Find the probability that a single randomly selected value is
between 29.1 and 30.2.
P(29.1<x<30.2)= ___?
Find the probability that a sample of size n=194n=194 is
randomly selected with a mean between 29.1 and 30.2.
P(29.1<¯x<30.2)= ___?
2.) Scores for a common standardized college aptitude test are normally distributed with a mean of 500 and a standard deviation of 98. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect.
If 1 of the men is randomly selected, find the probability that
his score is at least 583.3.
P( xx > 583.3) =
If 5 of the men are randomly selected, find the probability that
their mean score is at least 583.3.
P( ¯xx¯ > 583.3) =
In: Statistics and Probability
According to an international aviation firm, fatal accidents occur in just around one in every five million flights. With about 100,000 flights per 24 hour day worldwide, this means fatal accidents happen at a rate of 1 per 50 days. This translates to an average of 0.6 accidents per month. Assume that the number of fatal air accidents worldwide follows a Poisson distribution with λ=0.6 per month.
In: Statistics and Probability
According to an international aviation firm, fatal accidents occur in just around one in every five million flights. With about 100,000 flights per 24 hour day worldwide, this means fatal accidents happen at a rate of 1 per 50 days. This translates to an average of 0.6 accidents per month. Assume that the number of fatal air accidents worldwide follows a Poisson distribution with l=0.6 per month.
In: Statistics and Probability
Time Between Ship Arrivals (days) Probability
1 0.05
2 0.10
3 0.15
4 0.25
5 0.25
6 0.15
7 0.05
1.00
The time required to fill a tanker with oil and prepare it for sea is given by the following probability distribution:
Time to Fill and Prepare (days) Probability
2 0.10
3 0.30
4 0.40
5 0.20
1.00
A1:A10 = the departure times of tankers 1:10
B11 = the arrival time of tanker 11
In: Statistics and Probability
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) The probability that an employee at a company eats lunch at
the company cafeteria is 1) 0.32. The probability that an employee
is female is 0.62. The probability than an
employee eats lunch at the employee cafeteria and is female is
0.21. What is the
probability that a randomly chosen employee either eats at the
cafeteria or is female?
2) In a recent article it was reported that 27.3% of all college
students party during 2) weekdays, and 67% of these students plan
on going to graduate school. What is the probability that a
randomly-selected student party during weekdays and plans on
going to graduate school?
3) There are five men and four women working on a project. To handle one particular 3) aspect of the project, a subcommittee needs to be formed. In the interest of balance, it is decided that the subcommittee will consist of two men and two women. How many combinations of this subcommittee are possible?
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A student has access to professor evaluations. Overall, he has
enjoyed 70% of all classes he has taken. He finds that of the
courses he has enjoyed, 13% were taught by professors with poor
evaluations. 84% of the courses he has taken were taught by
professors with good evaluations.
4) What is the probability that the class was taught by a professor with good evaluations 4) and that the student enjoyed the class?
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey about US policy in Iraq, 62 % of the respondents
said that they support US policy in Iraq. Females comprised 53% of
the sample, and of the females, 46% supported US policy in Iraq. A
person is selected at random.
5) What is the probability that the person we select is female and supports U.S. policy in 5) Iraq?
6) Are the events "does not support U.S, policy in Iraq" and "female" statistically 6) independent? Why or why not?
7) Suppose we select a supporter of US policy in Iraq, what is the probability that the 7) person we select is female?
8) Suppose we select a person who does not support US policy in Iraq, what is the 8) probability that the person is male?
1
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
James' Surfboard Shop makes surfboards by hand. The number of
surfboards that James makes during a week depends on the wave
conditions. James has estimated the following probabilities for
surfboard production for the next week.
Number of Surfboards 5 6 7 8 9 10 Probability 0.13 0.22 0.31 0.17 0.13 0.04
Let A be the event that James produces more than seven surfboards. Let B be the event that James produces exactly six surfboards.
9) What is the probability of event A? 9)
10) What is the probability of the complement of A? 10)
11) What is the probability of the intersection of events A and B ? Why? 11)
12) Are events A and B collectively exhaustive? Why? 12)
13) The probability that a new small business closes before the
end of its first year is 42%. 13) In addition, 37% of all new
businesses are started by women. The probability that a
new business is either owned by a woman or goes out of business is
62%. Your sister
starts a new business. What is the probability her business will
still open at the end of
the first year?
14) In a survey of top executives, it was found that 17% had
traveled internationally 14) on business. The probability of one of
these executives fluently speaking a foreign
language was found to be 10%. The probability that one of these
executives neither
spoke a foreign language nor had traveled internationally was 0.81.
What is the
probability that an executive who speaks a foreign language has traveled internationally?
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Consider a sample space defined by events A1, A2, B 1, B2. Let P
(A1) = 0.40 , P (B 1 ! A1) = 0.60 and P (B 1 ! A2) = 0.70
15) What is P(A2)?
16) What is P(A1 "B1)? 17) What is P(A1 "B2)? 18) What is P(A2
"B1)?
15) 16) 17) 18)
Thanks, please show all work!
In: Statistics and Probability