STA2300 Data Analysis - Tutoring 2

Question 5 (14 marks)
The daily travelling time of the staff of a large corporation to come to the office is a random variable. Based on the historical record on the travelling time of the staff over the years it is found that the mean and standard deviation of daily travelling time are 35 minutes and 6 minutes respectively. Assume that the distribution of the daily travelling time of the staff follows a normal model. For a random sample of the daily travelling times of 9 staff, answer the following questions.

1. (1 mark) What is the variable of interest in the question?
2. (3 marks) Find the probability that the randomly selected daily travelling time of one member of staff will be less than 32 minutes.
3. (3 marks) What type of distribution is the sampling distribution of sample mean of the daily travelling time? Specify the parameters of this distribution for a random sample of the daily travelling times of 9 staff of the corporation, and write the values of those parameters in this context.
4. (5 marks) Find the probability that the sample mean of the random sample of daily travelling times of 9 staff will be less than 32 minutes.
5. (2 mark) Explain the reason for the difference in your answers in parts (b) and (d).