Quantitative Analysis

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Final Assignment Take-Home Exam – Example Solutions
QUANTITATIVE ANALYSIS AND BUSINESS DECISION MAKING
Question 1 – 5 Points
Leila took a standardized test and was told that her score was in the 89th percentile. Explain clearly and in only one sentence what this means. Notes:

 Percentiles are a way of describing the position of a particular score within a set of scores  As per the question, I was looking for one simple sentence to explain the meaning of the statement Ideal Answer: If Leila’s score was in the 89 percentile this means that Leila scored higher than 89% of participants in the test. th

Question 2 – 10 Points
A gas station near the Emirates Road is revaluating its gasoline-fuel reorder point. The gasoline fuel level in its main tank triggers an automatic replenishment order. The daily demand faced by the station for gasoline is normally distributed with an average of 8,000 liters and standard deviation of 2,500 liters. After the automatic order is placed, the gasoline-fuel is received at the gas station in exactly 3 days. In other words, it takes three days lead time for the gasoline to be replenished after the order has been made. At what volume should the re-order point be set to ensure that the station’s chance of being out of stock during the replenishment period is limited to a probability of 5%? Notes:

 Those people who did not score full points on this question usually made it more complicated than it is.  This question is very similar to many exercises we did together in class. The only complication is the three days of lead time – which was added to make the question more realistic for an actual business situation. Ideal Answer: µ = 8000; S = 2,500; Alpha = 0.05

 The average consumption is 8000l, with a standard deviation of 2,500l.  In order to identify the range of daily usage that has a 95% probability of occurring, we need to look at the range +/- two standard deviations = 3,000l to 13,000l

 In order to ensure we don’t go out of stock we need to take into account the maximum likely usage of fuel per day that includes 95% of possible outcomes = 13,000l (not 3000l)

 In order to make sure we don’t go out of stock for 3 days we need to assume that the maximum amount of fuel is used for 3 days = 3 x 13,000 = 39,000l

 Therefore, in order to ensure that we have only a 5% chance of going out of stock when it takes 3 days for the fuel to arrive, we need an automatic replenishment order to be placed when the level in the fuel tank reaches 39,000 litres. (Note: Some of you submitted the answer 36,300l based on calculating a one-tailed range. This answer also scored full marks, although I did not expect anyone to do this because we did not have the time to cover one-tailed ranges on the course).

Dr. Amanda Nimon Peters Nov 2012

Question 3 – 20 points – you may not exceed this page
Notes:

 The key to this question was the ability to pull useful observations from the data, and write those observations in a manner that would have clear meaning for senior management.

 There are many different perspectives that you could take on the data. The most useful would be to draw conclusions for the country/region in which you work, or the country/region that is most important for your business. Ideal Answer: These are just some examples of strong answers. There are many that are possible. Conclusions

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The survey found that on average across the Middle East, employees feel engaged and motivated in their current jobs (80% agreed they felt engaged; 74% agreed they felt motivated to perform well). In contrast, Middle Eastern workers appear to be less happy about the conditions of their employment. This is reflected in the lower levels of agreement to ‘feeling that the organisation deserves their loyalty’ (60%). Further, while they said they would speak highly of their organisations’ products and services (74%); there was a noticeable drop in the number who would speak...
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