Question 1 (Total of 21 marks)
An ice-cream shop is gathering feedback on the new flavours and toppings introduced for the last few days. A simple random sample of 260 customers were asked what new flavour they like best and with which topping. The preferences of these respondents are summarised below:
|
Flavour |
Topping |
|||
|
Lychee pearl |
Almond flake |
Caramel fudge |
Total |
|
|
Lime mint |
35 |
24 |
28 |
87 |
|
Mango yoghurt |
27 |
51 |
32 |
110 |
|
Cereal milk |
18 |
20 |
25 |
63 |
|
Total |
80 |
95 |
85 |
260 |
(a) (4 marks)Use Excel to obtain a 100% stacked column chart for the data in the table above. Make two general observations from the chart.
EXCEL Instructions: Refer to Topic 6 in the Excel Supplement Booklet for instructions on how to obtain 100% stacked column chart using the Assignment 2 data file.
(b) (2 mark)What is the probability that a respondent prefers Mango yoghurt?
(c) (2 mark)What is the probability that a respondent prefers Cereal milk AND Lychee pearl topping?
(d) (2 marks)What is the probability that a respondent prefers Lime mint OR Almond flake?
(e) (3 marks)Given the preferred topping is Caramel fudge. What then is the probability the flavour chosen is Lime mint?
(f) (3 marks)Given the preferred flavour is Cereal milk. What then is the probability the topping chosen is Lychee pearl?
(g) (5 marks)Are the events Mango yoghurt and Topping statistically independent of each other?Show all calculations to support your answer.
Question 2 (Total of 18 marks)
Samantha is the manager of the Bendigo Bank East branch in central plaza. She would like to investigate complaints of long queues in her branch to improve customer experience. To analyse the waiting time, Samantha observed and recorded the waiting time (mins) of customers at the counter in
