Solved: ABCD Statistics Questions
- ABCD is a fast food restaurant, and has a number of franchisers across the South Wales regions. Recently the Head Office of ABCD received a number of complaints from customers that the queuing time is too long. Each franchiser has randomly chosen 100 customers and recorded their waiting time until food is served. The results are shown in table 1.
(a) What is the average waiting time (arithmetic mean) for each franchiser? Which franchiser has the shortest/longest waiting time?
(b) What is the overall average waiting time and standard deviation? Which franchiser should improve their performance and why.
(c) The Head Office wants to know what the most occurring waiting time in each franchiser is. Explain the concept of the mode, mean, and median and help managers of each franchiser find the right number to report back to the Head Office.
2. ABCD is investigating an option to invest in an online booking system, where customers can order food prior to their visit. The management team is thinking of either developing a mobile app or booking through their website. Before making the final decision, the company conducted a pilot study using both platforms to explore the relationship between online orders and sales revenue. Orders (x) are in 000s and sales revenue (y) is in £000s. Summary data for 6 franchisers was as follows;
(a) Calculate correlation coefficient, r, for each options, clearly showing
calculations, and explain the meaning
(b) Calculate the equation of the least squares regression line (i.e. y = a + bx).
(c) The market research shows that if the company introduces the online booking system, there will be an increase of orders to 20,000. In this case, what might be the estimated sales revenue if there is (a) a Mobile App, and (b) a Website booking? Which system should the company develop?
3. ABCD has field-tested two booking platforms – Mobile App and Website on 1,000 volunteers. At a test volunteers were asked to order their food using the Mobile App and Website system, and asked to rate each system. The results of the test are as follows.
| Mobile App | Website | |
| Easy to navigate | 385 | 245 |
| Easy to Order | 265 | 105 |
Calculate the following probabilities:
(a) that a volunteer who has said that it was easy to navigate
(b) that a volunteer who used the Website and has said that it was easy to order
(c) that a volunteer has used the Mobile App, given that the person said it was easy to order
(d) Based on findings, suggest what system the company should develop to improve customer experiences.
4. ABCD reviewed how much customers spend per order. It has found that the overall spending can be said to be normally distributed with a mean of £22 and a standard deviation of £5.
(a) What percentage of customers have spent less than £15?
(b) As a part of promoting the new online booking system, the company is thinking of offering discount on top 10% of most spent customers. If a customer wants to receive the discount offer, what’s the minimum amount they have to spend on the order?
(c) What if a standard deviation of the sample is £10 instead of £5, how would it affect their discount offer? Would this be a good deal for customers?
Solutions
Question 1:
What is the average waiting time (arithmetic mean) for each franchiser? Which franchiser has the shortest/longest waiting time?
The arithmetic mean can be calculated using the formula when dealing with grouped data
=∑mf/n
Where: m is the class midpoint
Worked out Solutions
Means:
Cardiff = 8.05
Newport = 6.2
Swansea = 8.2
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