1. Thirty students in the School of Business were asked what their majors were. The following represents their responses (M = Management; A = Accounting; E = Economics; O = Others). [You can use the attached Excel file 'Majors' to solve this problem].
A M M A M M E M O A
E E M A O E M A M A
M A O A M E E M A M
a. Construct a frequency distribution
b. Construct a relative frequency distribution.
c. Draw an appropriate graph.
2. You are given the following data on the ages of employees at a company.
26 32 28 45 58
52 44 36 42 27
41 53 55 48 32
42 44 40 36 37
a. Construct a stem-and-leaf display.
b. Comment on the shape of the distribution.
3. Travel + Lesure magazine presented its annual list of the best hotels in the world. A sample of 12 of the top-rated hotels in the US is given in the file 'Travel'.
a. Produce descriptive statistics for the number of rooms and cost per night. Briefly interpret your results.
b. Develop a graph to show the relationship between the number of rooms and the cost per night (note: cost is the dependent variable). Discuss.
c. What is the correlation coefficient? What does it tell you about the relationship between the number of rooms and the cost per night? Does this appear reasonable? Explain.
4. Suppose annual salaries for sales associates from a particular store have a mean of €32,500 and a standard deviation of €2,500.
a. Calculate and interpret the z-score for a sales associate who makes €36,000.
b. Use the Chebyshev's theorem to calculate the percentage of sales associates with salaries between €26,250 and €38,750.
c. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between €27,500 and €37,500.
d. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes €42,000. Should this salary be considered an outlier? Explain.
5. Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the projects is 0.90.
a. What is the probability that she will get both projects?
b. Are the events of getting the two projects mutually exclusive? Explain, using probabilities.
c. Are the two events independent? Explain, using probabilities.
6. John parks cars at a hotel. On the average, 6.7 cars will arrive in an hour. Assume that a driver's decision on whether to let John park the car does not depend upon any other person's decision. Define the random variable x to be the number of cars arriving in any hour period.
a. What is the appropriate probability distribution for x? Explain how x satisfies the properties of the distribution.
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.
7. The salaries at a firm are normally distributed with an average salary of €19,000 and a standard deviation of €4,000.
a. What is the probability that an employee will have a salary between €12,520 and €13,480?
b. What is the probability that an employee will have a salary more than €11,880?
c. What is the probability that an employee will have a salary less than €28,440?
8. The university found that 20% of its students withdraw without completing the statistics course. Assume that 20 students are registered for the course.
a. Compute the probability that exactly four will withdraw.
b. Compute the probability that more than three will withdraw.
c. Compute the expected number of withdrawals.