Question 1 25 Points John is a final year student in Bath Spa University. He would like to set up an ice cream stall on campus. He has had some experience working in an ice cream shop and knows how to make ice cream. But he hasnt had any experience in setting up a business. He is taking some advice from you who are studying the degree in Business and Management. a.John needs to fix a menu. He wants to know the most popular flavours among students. Explain to John the best data source to get this information and list three methods that he can use to collect the information. (4 marks) b. John collected the below data using one of the suggested methods. He reproduced the raw data into the below table. -Create a chart to show the number of votes for each flavour. (2 marks) -Whats the most popular flavour? And how much is the relative frequency of this most liked flavour? (2 marks) Flavours of ice cream No. of votes Plain vanilla 42 Diary cream 12 Rum 8 Mint and chocolate 26 Toffee 34 Diary cream and Oreo 38 Strawberry 47 Walnut 20 Raspberry 19 (4 marks) c.After the initial market research, John decided to offer 2 flavour on his menu. They are strawberry, and diary cream and Oreo. John will rent the university onsite kitchen and make the ice cream freshly in his kitchen. One portion of strawberry ice cream requires 40ml (0.04L) strawberry syrup, 300g (0.3kg) of cream and 150g (0.15kg) of sugar. One portion of diary cream and Oreo ice cream requires 400g (0.4kg) of cream, 90g (0.09kg) of Oreo biscuits and 180g (0.18kg) of sugar. It costs John 1 minutes and 30 seconds to make 1 portion of strawberry ice cream and 3 minutes to make diary cream and Oreo ice cream. Every strawberry ice cream makes 2.5 gross profit while every diary cream and Oreo ice cream makes 3 gross profit. John wants to make at least 100 portions of strawberry ice cream and at least 60 portions of diary cream and Oreo ice cream every week. Every week, John plans to work 10 hours. He wants to order the minimum amount of raw materials from the wholesaler at the beginning of the business. The wholesaler requires the weekly minimum order Unit: As specified Strawberry syrup L Cream kg Oreo biscuits kg Sugar kg 8 100 18 48 John is able to sell as much as he can produce every week according to the initial market research. Based on the information above, please help John to find the optimal production strategy (i.e. the maximum gross profit he could achieve every week.) Use the linear programming - the graphical approach to resolve the question. Marks will be awarded to each step. (14 marks) d.Based on your answer above, what are the surplus raw materials every week and how much are the leftovers? Can you give some advice to utilise the leftovers? (3 marks)

Question 2 25 Points 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 has student loan to support his living and tuitions. The loan doesnt require to be repaid until he finds his first full-time job. Mike wants to save 200 per month i.e. 2,400 per annum from the part time job. He transfers the 2,400 into his saving account at the end of every year. As to the below Accommodation Expenses table published by the Students Union, the below students were randomly selected to help understand the weekly accommodation expenses and distance to campus. Whats the probability for Mike to spend over 160 weekly on accommodation based on the information in the table? The table contains weekly data. Distance to Campus (miles) (Accommodation to Campus) Amount spent, 0.1 to 0.25 0.26 to 4.0 Over 4.0 Below 100 0 0 2 101 - 120 0 12 20 121 - 140 0 65 0 141 - 160 23 54 1 161 - 180 38 42 0 181 - 200 23 5 0 Above 200 5 1 0 (4 marks) How much is the frequency for students living over 0.26 to 4 miles away from the campus? (3 marks) As to the category of Amount Spent, , what is the modal group? (4 marks) Assuming Mike is saving the same amount every year in the next 6 years. The time is Jan 01, 2020. How much will be the balance on Mikes saving account on Dec 31, 2025, if his saving account pays simple interest rate 3% per annum and Mike always keeps the interest in his saving account? (5 marks) Assuming Mike is saving the same amount every year in the next 6 years. The time is Jan 01, 2020. How much will be the balance on Mikes saving account on Dec 31, 2025, if his saving account pays compounding interest rate 3% per annum and Mike always keeps the interest in his saving account? (9 marks)

Question 3 25 Points 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% (the opposite is the highest 70%.) 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. What mark (to the nearest whole number) must a candidate achieve in order to secure an interview? Show your workings. (3 marks) Explain the characteristics of standard normal distribution and normal distribution, respectively. (7 marks) 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 (measured in grams) distributes as the below diagram. What is the distribution as described in the below chart and probability density function of the distribution in the chart? (5 marks) What is the mean and standard deviation of this distribution, respectively? (5 marks) What is the probability of a candidate taking salad between 13 16 grams? (5 marks)

Question 4 25 Points The below data represent the advertising expenditure and sales of Liu Liu Ltd from year 2010 to 2019. Table: Advertising Expenditure vs. Sales from 2010 to 2019 Year Advert. Expenditure Sales Growth rate of Ad. Expenditure Growth rate of Sales (x, 000) (y, 000) 2010 19 84 2011 22 108 18% 29% 2012 32 82 46% -24% 2013 42 86 32% 6% 2014 47 84 11% -3% 2015 46 94 -2% 11% 2016 58 103 27% 10% 2017 63 115 8% 12% 2018 70 106 11% -8% 2019 80 142 15% 34% Total 478 1003 What is the statistical relationship shown in the table and list out 3 characteristics of this relationship? (4 marks) Work out and explain the values of parameters of the relationship described in the table (i.e. work out the equation of the relationship and coefficient of determination) and show the relationship in a chart. (10 marks) How much is the average of growth rate of Ad. Expenditure and growth rate of sales, respectively? Show your workings and explain your choice of mean used. (8 marks) Explain the relationship and make recommendation to Liu Liu Ltd based on the information given. (3 marks)