A local restaurant allows its serving staff to receive tips from the customers. Based on the historical record on
the daily tips received by the serving staff over the years it is found that the mean and standard deviation of daily tips are $27.35 and $6.28 respectively. Assume that the distribution of amount of daily tips received by the serving staff of the restaurant follows a normal model. For a random sample 16 daily tips from the population of daily tips of the restaurant, answer the following questions.
(a) (1 mark) What is the variable of interest in the question?
(b) (3 marks) Find the probability that one randomly selected daily tip will be less than $25.00.
(c) (3 marks) What is the sampling distribution of sample means of the amount of daily tips? Specify the parameters of this distribution for a random sample of 16 daily tips from the population of all daily tips of the restaurant.
(d) (5 marks) Find the probability that the sample mean of the random sample of 16 daily tips will be less than $25.00.
(e) (2 mark) Explain the reason for the difference in your answers in parts (b) and (d).