Nationwide, the amount charged by doctors for performing a particular minor surgical procedure averages $1220 and varies with a standard deviation of $300. We randomly select 100 bills from the population of all bills charged for this surgery. Let X represent the average amount charged for these 100 surgical procedures.

a) Find the mean and standard deviation of the sample mean or X ?

b) Find the probability that the average amount charged over these 100 procedures is more than $1200?

c)Find the probability that the average amount charged over these 100 procedures is between $1200 and $1250?

d) The 95% confidence interval for the true average surgical charge is between what to values? Use X=1200.

Please show your work.