A survey is carried out to study the number of hours, X, per day spent on using the Internet by the customers of an Internet Service Provider(ISP). Responses from 15 randomly selected customers give the following data:

3 2 5 6 1 5 3 4 5 2 4 5 9 5 1

(a) Determine the mean and variance of the data set. (4 marks)

(b) Is there an outlier in the data set? Justify your answer. (6 marks)

(c) Suppose a selected customer is found to spend at most 5 hours on using the Internet. What is the probability that this customer spends more than 3 hours on using the Internet? (4 marks)

(d) Suppose the customer service manager of the ISP discovers that one data point has been mistakenly recorded to 4, and that data point should be less than 4. State whether the mode, median and mean of the correct sample become smaller than, greater than or the same as those of the incorrect sample. Explain your answer.