A company offers medical insurance to its employees. A recent study by the HR manager shows the annual medical cost incurred by employees is normally distributed with a mean of $1,280 and a standard deviation of $420. The HR manager is concerned over the increasing cost of medical insurance to the company in recent years. Only for part d, it will require a diagram. Thank you.

(a) State the variance and how the normal curve will change when the mean increases and the standard deviation increases.

(b) Calculate, with the help of a diagram, the percentage of the employees who incurred more than $1,500 in annual medical cost.

(c) Calculate, with the help of a diagram, the amount for the top and bottom kth percentage of the population, where k is your register number in your class register.

(d) The following probability statement describes the annual medical cost incurred by employees. Calculate the value of C with the help of a diagram. P ( $1,000 < annual medical cost < C )=0.5