Assignment:
The U.S. Bureau of Labor Statistics reports that the average annual salary in the metropolitan Boston area is $50,000. Suppose annual salaries in the metropolitan Boston area are normally distributed, with a standard deviation of $5,000. A Boston area worker is randomly selected. Use this information for questions 1 through 5.
1. What is the mean of the distribution?
2. What is the z score for a worker's annual salary of $55,000?
3. What is the probability that a worker's annual salary is greater than $55,000?
4. What is the probability that a worker's annual salary is between $50,000 and $60,000?
5. What is the salary of a worker who represents the 75th percentile ? (estimate is in thousands)
Many universities require students to take an aptitude test, like the American College Test (ACT), before entering college. They also require students to take the Graduate Requirement Test (GRE) before entering graduate school. Both tests are normally distributed. Use the information below and a student's exam scores to answer questions 6 and 7.
|
Exam Administered
|
Mean
|
Standard Deviation
|
Student's Score
|
|
ACT
|
18
|
6
|
20
|
|
GRE
|
500
|
100
|
450
|
6. What percentage of the population scored better than this student on the GRE?
7. The student performed better on the GRE.
8. Determine which distribution you would use to analyze the following problem.
In a recent study, it was determined that 20% of all stock investors are retired people. Suppose a random sample of 25 stock investors is taken. What is the probability that exactly 7 are retired people?
9. A recent poll at a university found that 40% of the students were registered to vote. What is the probability that no students, out of the next 10 students, will say they are registered to vote?
10. A recent poll at a university found that 40% of the students were registered to vote. What is the probability that at least 3, out of the next 10 students, will say they are registered to vote?
11. A recent poll at a university found that 40% of the students were registered to vote. On average, how many out of the next 10 students would you expect to be eligible to vote?
12. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows. What is the average number of service calls?
|
Number of Service Calls
x
|
Probability
P(x)
|
|
0
|
0.20
|
|
1
|
0.10
|
|
2
|
0.05
|
|
3
|
0.10
|
|
4
|
0.05
|
|
5
|
0.50
|
13. A popular airline travels between San Antonio and Phoenix. Suppose we believe that actual flight times are uniformly distributed between 110 minutes and 150 minutes. What is the average flight time between these two cities?
14. A popular airline travels between San Antonio and Phoenix. Suppose we believe that actual flight times are uniformly distributed between 110 minutes and 150 minutes. What is the probability that the flight will arrive after 125 minutes?
15. A popular airline travels between San Antonio and Phoenix. Suppose we believe that actual flight times are uniformly distributed between 110 minutes and 150 minutes. What is the probability that the flight will arrive between 125 minutes and 145 minutes?
16. A popular airline travels between San Antonio and Phoenix. Suppose we believe that actual flight times are uniformly distributed between 110 minutes and 150 minutes. What is the probability that the flight will arrive exactly 140 minutes after departure?
17. Determine which distribution you would use to analyze the following problem.
Seventy percent of American workers say job stress caused frequent health problems. Suppose a random sample of 100 American workers is selected. Which distribution would you use to determine the probability that more than half of them would say job stress is the cause of frequent health problems?
18. A real estate office sells 2.6 houses on an average weekday and sales of houses on weekdays are Poisson distributed, what is the probability of selling exactly two houses in one day?
19. A real estate office sells 2.6 houses on an average weekday and sales of houses on weekdays are Poisson distributed, what is the probability of selling no houses in one day?
20. A real estate office sells 2.6 houses on an average weekday and sales of houses on weekdays are Poisson distributed, what is the probability of selling more than two houses in one day?