Applied Quantitative Analysis

Question 1

Given here are the mean and median annual salaries of sales representatives employed by two competing travel companies A and B.

 

                         Company   
        A     B
Mean Salary    $63,500 $65,000
Median Salary    $64,000 $62,000

 

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Assume that the salaries are set in accordance with job competence and the overall quality of sales representatives is about the same in the two travel companies.

  1. Which company offers a better prospect to a sales representative having superior ability? Explain your answer.
  2. Where can a medium-quality sales representatives expect to earn more? Explain your answer.

Question 2

Each salesperson at Cherry Tree Hospitality Service is rated either below average, average, or above average with respect to sales ability.  Each salesperson is also rated with respect to his or her potential advancement – either  fair, good, or excellent.  These traits for the 500 salesperson in this large corporation were cross-classified into the following table. You must show your work for this problem 

                                                      Potential for  Advancement

Sales Ability                          Fair               Good             Excellent

 Below average                        16                   12                     22

Average                                  45                   60                     45

Above average                        93                   72                   135

  1. What is the probability a salesperson selected at random will have above average sales ability and excellent potential for advancement? 
  2. What is the probability a salesperson selected at random is rated with  average sales ability or fair potential for advancement?

Question 3

The Dow Jones Industrial Average has reached 27,164 points this week.  An investment advisor specialized in Travel Company stocks predict that the stocks of five travel companies she is following will rebound in the next 18 months.  From this advisor’s records on stock picks, 40 percent of the stocks she recommends are profitable.

Required:      

  1. What is the probability that no more than one of the five stocks are profitable?
  2. What is the probability that at least three of the five stocks are profitable?

Question 4

Seven food experts rated a newly developed fast food menu on a scale of 1 to 50. Their ratings were: 34, 41, 26, 29, 32, 36, and 40.

Required:

  1. What is the mean rating?
  2. What is the standard deviation?
  3. A second group of experts rated the same fast food menu.  The mean was 35.7, and the standard deviation 6.3. Compare the ratings with those of the first group of experts. What conclusion can you draw from the ratings by the two groups of experts regarding their opinions of this new fast food menu?

Question 5 

 The weekly amount spent by an event management company for travel has approximately a normal distribution with a mean of $2,500 and a standard deviation of $400.  If $3,000 is budgeted to cover next week’s travel expenses

Required:

What is the probability that the actual expenses will exceed the budgeted amount?

  1. b. how much should be budgeted each week so that the probability is only 0.05 that the actual expense will exceed the budgeted amount?

 

 

 

Question 6

  1. A hotel manager must distribute salary raises for next year.  She has decided that the mean raise is to be $2,000, the standard deviation of the raise is to be $400, and the distribution approximates normally.

Required:

  1. the highest 10% of the employees (ranked by merit) will have a raise equal to or greater than $___________.
  2. b. the 5% of the employees with the lowest merit rating will receive no more  than $__________ each.

 

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