Problem Set Three 2015

EMBA 7100: Problem Set Three

!

Show all work necessary to arrive at answers on this worksheet and then post answers to the web site provided before the class meeting where the problem set is due.

!
!

Question 1: Americans have become increasingly concerned about the rising cost of Medicare.
In 1990, the average annual Medicare spending per enrollee was $3267; in 2003, the average annual Medicare spending per enrollee was $6883. Suppose you hired a consulting firm to take a sample of fifty 2003 Medicare enrollees to further investigate the nature of expenditures.
Assume the population standard deviation for 2003 was $2000. What is the probability the sample mean will be within +-$300 of population mean?

!
!
!
!
!
!
!
!
!
!
!
!
!
!

Question 2: Referring to Question 1, what is the probability the sample mean will be greater than
$7500?

!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

Question 3: The mean television viewing time for Americans is 15 hours per week. Suppose a sample of 60 Americans is taken to further investigate viewing habits. Assume the population standard deviation for weekly viewing time is 4 hours. What is the probability the sample mean will be within 1 hour of the population mean?

!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

Question 4: Referring to Question 3, what is the probability the sample mean will be within 45 minutes of the population mean?

!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

Question 5: A production process is checked periodically by a quality control inspector. The inspector select random samples of 30 finished products and computes the sample mean product weights. If test results over a long period of time show that 5% of the sample mean values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and standard deviation for the population of products produced with this process?

!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!

Question 6: In an effort to estimate the mean amount spent per customer for