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Unformatted text preview: Summer Session II, Math 111, Sec. 0202. 08/22/03
E.G.K. Lopez—Escobar
. NAME ......................................... ..
PROLOGUE Please read the following instructions: Answers without supporting evidence carry little weight.
Calculations without a deﬁnite answer to the problem carry little weight. Nothing is to be written on the section of the page reserved for the
statement of the problem. The answer(s) to the problem is(are) to be given (in the form of ab—
breviated English sentences) in the section of the page reserved for the
answers. Calculations, or justiﬁcations, for your answer(s) should not
be on the same side of the page as the statement of the problem. The calculations (justiﬁcations) should be written starting on the back
side of the page on which the problem is stated. Although the calculations (or justiﬁcations) need not be written as
complete sentences of English, nevertheless it should be obvious to the
reader What you are calculating (justifying). Beware that blatantly
false or nonsensical statements will signiﬁcantly lower your grade. The student is expected to check the given answer(s) and calculations. It is recommended that the student read all the problems in the exam—
ination before attempting to ﬁnd the solutions. It is not required that Problem 1 should be the ﬁrst problem attempted. Failure to follow the above instructions may lower your grade. After reading the instructions initial the following statement: I have read the above instructions . . . . . . . . . . . . . .. Problem 1 A woman purchased a $50,000, 1yr term life insurance policy for $500.
Assuming that the probability that she will live another year is 0.9935, ﬁnd
the company’s expected gain. Answer: ________ ___W.m____.%_f__ Problem 2 The probability that an airplane engine will fail in a certain route is
0002. Assuming that engine failures are independent of each other, what is
the probability that a four engine plane will experience exactly two engine
failures on that route? W. Answer: Problem 3 By how many tickets should a 400 passenger ﬂight be overbooked if 5%
of the ticketed passengers are usually 7’noshovvs” and a person should have
a 98% probability of being seated in the ﬂight? W
Answer: ____________ _~_..r.~..i________.._7____________________.__f___.mw Problem 4 The scores in an examination are normally distributed with a mean of 75
and a standard deviation of 15. If 5% of the class is to be assigned an ”A”,
what is the lowest score a student may have and still obtain an “A”? W
Answer: ______________ _____T_._.M________T~.~_ Problem 5 In a manufacturing plant, four machines, a, ﬂ, 7 and 6, produce 20%,
25%, 30% and 25%, respectively, of the total production. The production of
machine a is 1% defective, for machine ﬂ it is 1.5%, for machine 7 it is 1.75%
and for machine 6 it is 2%. If an item is selected at random and found to be
defective, What is the probability that it was produced by machine 7? W
Answer: _______ _________________,_.T_______________________._______ ...
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 Spring '08
 staff
 Normal Distribution, Standard Deviation, .........

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