Statistics Exam Paper
08 ETHE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
First Semester Examination 2010
QUANTITATIVE RESEARCH METHODS
(STAT1008)
Writing Period: 3 hours duration
Study Period: 15 minutes duration
Permitted Material: Non-programmable calculator, dictionary and 1 A4 page with notes on both sides
Instructions to Candidates:
• Attempt ALL questions.
• Each question is of equal mark value.
• Start your solution to each question on a new page.
• To ensure full marks show all the steps in working out your solution. Marks may be deducted for failure to show appropriate calculations or formulae.
• Unless otherwise stated, use a significance level of 5%.
• Selected statistical tables are attached to the back of the examination paper.
Page 1 of 9
Question 1 (25 marks)
Many companies have invested in automated customer-service systems for phone calls, primarily because the cost of a phone call passed on to a live operator is approximately ten times that of a call answered by an automated system. However, many customers dislike automated systems, and will choose the first offered option to speak with a live person, for example, pressing “0” at the “Press 0 to speak with a customer service representative”. Research shows that approximately 40% of callers to automated systems will automatically opt to speak to a live operator when given the chance. Imagine that 10 independent callers contact an automated customer service system.
(a) (3 marks) What type of random variable is the number of callers who automatically opt to talk to a live operator? Give the appropriate parameters of the random variable.
(b) (1 mark) What is the probability that none of them automatically opts to talk to a live operator?
(c) (1 mark) What is the chance that 3 or fewer will automatically opt to talk to a live operator?
(d) (2 marks) What is the chance that exactly 3 will automatically opt to talk to a live operator?
(e) (4 marks)
SCHOOL OF FINANCE AND APPLIED STATISTICS
First Semester Examination 2010
QUANTITATIVE RESEARCH METHODS
(STAT1008)
Writing Period: 3 hours duration
Study Period: 15 minutes duration
Permitted Material: Non-programmable calculator, dictionary and 1 A4 page with notes on both sides
Instructions to Candidates:
• Attempt ALL questions.
• Each question is of equal mark value.
• Start your solution to each question on a new page.
• To ensure full marks show all the steps in working out your solution. Marks may be deducted for failure to show appropriate calculations or formulae.
• Unless otherwise stated, use a significance level of 5%.
• Selected statistical tables are attached to the back of the examination paper.
Page 1 of 9
Question 1 (25 marks)
Many companies have invested in automated customer-service systems for phone calls, primarily because the cost of a phone call passed on to a live operator is approximately ten times that of a call answered by an automated system. However, many customers dislike automated systems, and will choose the first offered option to speak with a live person, for example, pressing “0” at the “Press 0 to speak with a customer service representative”. Research shows that approximately 40% of callers to automated systems will automatically opt to speak to a live operator when given the chance. Imagine that 10 independent callers contact an automated customer service system.
(a) (3 marks) What type of random variable is the number of callers who automatically opt to talk to a live operator? Give the appropriate parameters of the random variable.
(b) (1 mark) What is the probability that none of them automatically opts to talk to a live operator?
(c) (1 mark) What is the chance that 3 or fewer will automatically opt to talk to a live operator?
(d) (2 marks) What is the chance that exactly 3 will automatically opt to talk to a live operator?
(e) (4 marks)