# Sampling for Health Insurance A health services provider has been reimbursed by a national health in

Sampling for Health Insurance

A health services provider has been reimbursed by a national
health insurance organization for a large number of services It appears that
overpayments may have occurred on many of the reimbursements owing to errors
made during the billing process or to up-coding (billing for a more complicated
service than was actually provided) Overpayments in the past have been skewed,
with a standard deviation of \$1200 per service provided The health services
provider claims that no overpayments have occurred on average, that is, that
the actual mean overpayment is \$0 An audit of a random sample of 36
reimbursements was conducted, and the sample mean overpayment was \$400

a Determine the probability that a sample mean overpayment
is greater than or equal to that found in the audit if the provider’s claim is
true

b Determine the probability that the sample mean overpayment
for the audited reimbursements will be between \$200 and \$400 if the
provider’s claim is correct

c Determine the probability that the total overpayment to
the provider for the sampled reimbursements will be greater than or equal to
\$14400 if the provider’s claim is true