Question 1 (13 marks)

A population consists of three restaurants and their menu items has been recorded in a file, Restaurants.xlsx, which can be downloaded from on Moodle in Assessment block.

a) What is the population distribution of the number of menu items?

b) What are the mean and standard deviation of the population distribution in a)?

c) If a random sample with replacement of 2 restaurants is picked from the population, what is the sampling distribution of the sample mean number of menu items?

d) If a random sample without replacement of 2 restaurants is picked from the population, what is the sampling distribution of the sample standard deviation for the number of menu items?

e) What is the mean of the sampling distribution in d)?

f) Compare the mean of the population distribution obtained in b) and the mean of the sampling

distribution in c).