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.

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