Business management Quantitative methods

Quantitative methods

Business management

Question 1 (25 marks)After post-graduate study, Mike found a job as HR analyst in London. The company is
currently recruiting Chief Marketing Officer. The HR department recently sent out a
knowledge test to the applicants after the initial CV screening. At this stage of selection, the
company does not invite the lowest scoring 30% back for the next face-to-face interview.
According to the historical data, the test scores on this test are normally distributed and has
a mean of 70 with standard deviation of 10.
a. What mark (to the nearest whole number) must a candidate achieve in order to
secure an interview?
(3 marks)
b. How much is the 95% confidence interval for the test scores?
(7 marks)
c. The company offers free buffet lunch for candidates attending the interview. As a
HR analyst, Mike is asked to estimate the amount of salad to order for the interview
day. Sampling suggests that the amount of salad taken by each candidate distributes
as the below diagram. What is the distribution as described and probability density
function of the distribution in the diagram? What is the probability of the blue area
in the diagram? (15 marks)
Question 3 (15 marks) Business management Quantitative methods
Mike is a first year university student who is trying to understand his financial situation.
Mike currently lives 1.5 miles away from campus. He works part time in a retail centre that
pays him £800 per month. Mike saves £200 out of the part time job pay for his further
education plan.
a. As to the below Travel Expenses table published by the Students’ Union, 185
students were randomly selected to help understand the travel expenses and
distance to campus. What’s the probability for Mike to spend over £10 on journeys
to campus?
Distance to Campus (miles)
Amount spent, £ 0.1 to 0.25 0.26 to 1.0 Over 1.0
0 – 4.99 35 26 10
5.00 – 9.99 18 39 20
10.00+ 4 14 19
(3 marks)
b. How much is the frequency for students living over 1 mile away from the campus?
(3 marks)
c. As to the category of Amount Spent, £, what is the modal group?
(4 marks)
d. Assuming Mike is saving the same amount per month in the next 3 years. How much
does Mike get for his saving after 3 years, if his saving account pays simple interest
rate 3% per annum?
(5 marks)
Question 2 (60 marks): The answer to this question should be in the form of the 1500-word report
and should use the structure provided at the end. Marks are allocated both for the calculation and
how the interpretation is being presented. Business management Quantitative methods
The dataset provided shows how much GS Limited a global company spends on advertising (in 1000s
of pounds) and their sales in millions of pounds. Each datapoint shows the weekly spend/sales data.
Using the data provided, you are required to provide a report to the management to see which of
these channels are effective. This will help the management to decide on future investments so
ensure you have addressed the following points:
a. Provide descriptive statistics for each of the channels (min, max, mean, median,
standard deviation) and provide a brief explanation (20 marks)
b. Show the scatter diagram for each of the three channels and the line of best fit for
each (3X5 = 15 marks)
c. Do a linear regression for each of the three channels and explain your regression (15
marks)
d. Explain the relationship and make recommendation to GS Ltd based on the
information given. (10 marks)

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