The Human Resource department of a large corporate wants to understand the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in AUD) for the preceding year: $1110, $300, $250, $ 850, $510, $200, $1800, $425, $600, $180

Answer the following questions:

a)Calculate the arithmetic mean and the median.

b) Calculate the first quartile and the third quartile and interpret the results.

c) Calculate the interquartile range and interpret the result.

d) Is the sample of family dental expenses skewed? Briefly explain the reason. If the sample of family dental expenses is skewed, is it positively or negatively skewed?

e) Suppose the board of the company has decided that the feasibility of providing an employee dental insurance plan depends on the population mean of family dental expenses. Given that the sample standard deviation of family dental expenses is $510, construct a 95% confidence interval estimate of population mean of family dental expenses. Assume the population distribution of family dental expenses of the employees is normal distribution