James had a perception that the annual coffee consumption is most likely to be more than 3.2kg: Descriptive Analytics Assignment, NUS, Singapore

In a multicultural country like Singapore, coffee plays an important role in social interactions. People enjoy having a cup of coffee with friends or even business negotiations. James has been operating a premium coffee shop in the country. He has an intention to expand the shop into a coffee shop chain within the country. In order to understand the coffee culture in near future, he collected some information from a random sample of 150 coffee drinkers. The gender and annual coffee consumption (in kg) data are stored in
the Excel data file Assignment Data T2’24 (Re-assessment).

Question 2

James had a perception that the annual coffee consumption is most likely to be more than 3.2kg. A friend commented to James that there is a high percentage of heavy drinker in the country (consumption more
than 4.5kg).

Referring to the Excel output generated for Question 1 part (b), use the mean and standard deviation of coffee consumption to calculate the following probabilities by hand. Show all your workings.

Assume that the coffee consumption is normally distributed.

NOTE: Round the mean and standard deviation you obtained in Q1(b) to 2 decimal places before using them to do the calculation here.
(a) Calculate the probability that a randomly selected coffee drinker has coffee consumption of more than 3.2kg.
(b) What is the percentage of the coffee drinker that is considered heavy drinker according to the comment made by James’ friend?
(c) Are James’ perception and his friend’s comment well supported by the study?
(d) Use Excel function to find out the probability for part (b). Show the function used and the answer obtained.