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STAB22 Past Midterm solutions 03
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University of Toronto ScarboroughSTAB22 Midterm Examination
October 2008
For this examination, you are allowed one handwritten letter-sized
sheet of notes (both sides) prepared by you, a non-programmable,
non-communicating calculator, and writing implements.
This question paper has 12 numbered pages; before you start,
check to see that you have all the pages. There is also a signature
sheet at the front and statistical tables at the back.
This examination is multiple choice. Each question has equal
weight. On the Scantron answer sheet, ensure that you enter your
last name, first name (as much of it as fits), and student number
(in “Identification”).
Mark in each case the best answer out of the alternatives given
(which means the numerically closest answer if the answer is a
number and the answer you obtained is not given.)
Before you begin, check that the colour printed on your Scantron
sheet matches the colour of your question paper. If it does not,
get a new Scantron from an invigilator.
Also before you begin, complete the signature sheet, but sign it
only when the invigilator collects it. The signature sheet shows
that you were present at the exam.
1
, 1. There are two sets of numbers. Set A is 5, 5, 5, 5. Set B is 4, 5, 6, 7. Without doing any calculations,
what can you say about the standard deviations of the two sets of numbers?
(a) Sets A and B have about the same standard deviation.
(b) Set B has a smaller standard deviation.
(c) The only way to compare the standard deviations is to calculate them.
(d) * Set A has a smaller standard deviation.
2. What is the median of the values 7, 3, 0, 1, 6?
(a) 3.4
(b) * 3
(c) 6
(d) 0
3. A stringing machine is a device for adjusting the tension of strings in a tennis racket. Some tennis
players ask for a string tension of 65 pounds. The actual tension produced by the machine for the
rackets belonging to these players varies according to a normal distribution with mean 65 pounds
and standard deviation 2 pounds. Use this information to answer this question and the 2 following
questions.
What proportion of rackets (belonging to players asking for a string tension of 65 pounds) will have a
string tension of 67.5 pounds or more?
(a) 0.00
(b) about 0.50
(c) 1.00
(d) 0.89
(e) * 0.11
4. Using the information in Question 3, what proportion of rackets (belonging to players asking for a
string tension of 65 pounds) will have a string tension between 64 pounds and 67.5 pounds?
(a) * 0.59
(b) 0.89
(c) 0.11
(d) 0.70
(e) 0.31
5. For all rackets (belonging to players asking for a string tension of 65 pounds), there is a value x such
that 20% of rackets will have an actual string tension less than x pounds. What is x?
(a) 60.9
(b) 69.1
(c) 66.7
(d) 65
(e) * 63.3
2
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