Newark College has 240 full time employees who are currently covered under the school’s health care plan. The average out of pocket cost for the employees on the plan is $ 1,880 with a standard deviation of $ 515. Newark College is performing an audit of its health care plan and has randomly selected 30 employees to analyze their ­out of pocket costs.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than $ 1,825?

c. What is the probability that the sample mean will be more than $ 1,840?

d. What is the probability that the sample mean will be between $ 1,900 and $ 1,950?