STAB22H3 Final: STAB22 Final Exam 2013 Fall
UNIVERSITY OF TORONTO SCARBOROUGH
Department of Computer and Mathematical Sciences
DECEMBER 2013 EXAMINATIONS
STAB22H3 Statistics I
Duration: 3 hours
Last Name: First Name:
Student number:
Aids allowed:
- Two handwritten letter-sized sheets (both sides) of notes prepared by you
- Non-programmable, non-communicating calculator
Standard normal, tand the binomial distribution tables are attached at the end.
This test is based on multiple-choice questions. All questions carry 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 nu-
merically closest answer if the answer is a number and the answer you obtained
is not given.)
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.
There are 23 pages including this page and statistical tables. Please check to see you have
all the pages.
Good luck!!
Page 2 of 23
1. The events Aand Bare such that P(A)=2P(B), P(Aand B) = 0.08 and Aand B
are independent. Find P(Aor B).
A) 0.68
B) 0.6
C) 0.4
D) 0.52
E) 0
Solution: 0.08 = P(Aand B) = P(A)P(B) = 2P(B)2=⇒P(B) = √0.04 =
0.2 =⇒P(A) = 2 ×0.2 = 0.4 =⇒P(Aor B) = P(A) + P(B)−P(Aand B) =
0.4 + 0.2−0.08 = 0.52.
2. Historical evidence suggests that SAT scores are normally distributed with mean 1000
and standard deviation 180. What score (approximately) do you have to make to be in
the top 1 percent of all those who are taking this exam?
A) 586
B) 1180
C) 1234
D) 1325
E) 1415
Solution: Let X∼N(1000,180). P(X≥x) = 0.01. Solve P(Z≥z) = 0.01 =⇒
z= 2.325. So x= 1000 + 2.325 ×180 = 1418 . The closest is 1415.
3. Which of the following values is closest to the interquartile range for the standard normal
distribution?
A) 0
B) 0.5
C) 1.3
D) 2.5
E) 3
Solution: Q1=P25 ≈ −0.675 ; Q3=P75 ≈0.675; IQR =Q3−Q1= 0.675+0.675 =
1.35.
Page 3 of 23
4. The distribution of bachelor’s degrees conferred by a local college is listed below, by
major.
Major Frequency
English 2,073
Mathematics 2,164
Chemistry 318
Physics 856
Liberal Arts 1,358
Business 1,676
Engineering 868
Total 9,313
What is the probability that a randomly selected bachelor’s degree is not in Mathemat-
ics?
A) 0.232
B) 0.768
C) 0.303
D) 0.682
E) 0.889
Solution: P(not mathematics) = 1 −P(mathematics) = 1 −2,164
9,313 = 0.768.
5. The two-way table below classifies the members of a fitness club by gender and food
habits. Use this information to answer this question and the next question.
Women Men
Vegetarian 9 3
Non-vegetarian 8 10
If a member is selected at random from the club, what is the probability that this person
is a vegetarian female?
A) 3/4
B) 3/10
C) 1/10
D) 4/9
E) 9/17
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STAB22H3 Full Course Notes
Verified Note
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Document Summary
Two handwritten letter-sized sheets (both sides) of notes prepared by you. Standard normal, t and the binomial distribution tables are attached at the end. Scantron answer sheet, ensure that you enter your last name, rst name (as much of it as. Mark in each case the best answer out of the alternatives given (which means the nu- merically closest answer if the answer is a number and the answer you obtained is not given. ) 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. There are 23 pages including this page and statistical tables. Please check to see you have all the pages. Good luck: the events a and b are such that p (a) = 2p (b), p (a and b) = 0. 08 and a and b are independent. Page 2 of 23: 0. 68, 0. 6, 0. 4, 0. 52, 0.
