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ECEN 403 Probability and Statistics for Engineers Exercises

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CIVL/ECEN-403/MECH-328
Assignment # 4 Probability and Statistics for Engineers Summer 2019 - 20
Due Date: Sunday, August 30, 2020
Submit any 2 questions from Q1 - Q4, any 1 from Q5 Q7, any 1 from Q8 Q9,
any 2 from Q10 Q12, any 1 from Q13 Q14, and any 2 from Q15 Q17. (So,
total = 9 )
Following problems covers the topic on Binomial Distribution.
Q1: In a certain city district, the need for money to buy drugs is stated as the reason for
75% of all thefts. Find the probability that among the next 5 theft cases reported in this
district, (a) exactly 2 resulted from the need for money to buy drugs; (b) at most 3
resulted from the need for money to buy drugs.
Q2: According to a survey by the Administrative Management Society, one-half of U.S.
companies give employees 4 weeks of vacation after they have been with the
company for 15 years. Find the probability that among 6 companies surveyed at
random, the number that give employees 4 weeks of vacation after 15 years of
employment is (a) anywhere from 2 to 5; (b) fewer than 3.
Q3: In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the
trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find
the probability that (a) from 3 to 6 have blowouts; (b) fewer than 4 have blowouts; (c)
more than 5 have blowouts.
Q4: A nationwide survey of college seniors by the University of Michigan revealed that
almost 70% disapprove of daily pot smoking, according to a report in Parade. If 12
seniors are selected at random and asked their opinion, find the probability that the
number who disapprove of smoking pot daily is (a) anywhere from 7 to 9; (b) at most 5;
(c) not less than 8.
Following problems cover the topic on Multinomial Distribution.
Q5: The probabilities are 0.4, 0.2, 0.3, and 0.1, respectively, that a delegate to a certain
convention arrived by air, bus, automobile, or train. What is the probability that among 9
delegates randomly selected at this convention, 3 arrived by air, 3 arrived by bus, 1
arrived by automobile, and 2 arrived by train?
Q6: In a certain town, 40% of the eligible voters prefer candidate A, 10% prefer
candidate B, and the remaining 50% have no preference. You randomly sample 10
eligible voters. What is the probability that 4 will prefer candidate A, 1 will prefer
candidate B, and the remaining 5 will have no preference?

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Q7: According to a genetics theory, a certain genetics of guinea pigs will result in red,
black, and white offspring in the ratio 8:4:4. Find the probability that among 8 offspring,
5 will be red, 2 black, and 1 white.
Following problems cover the topic on Poisson Distribution.
Q8: In a certain industrial facility, accidents occur infrequently. It is known that the
probability of an accident on any given day is 0.005 and accidents are independent of
each other. (a) What is the probability that in any given period of 400 days there will be
an accident on one day? (b) What is the probability that there are at most three days
with an accident?
Q9: In a manufacturing process where glass products are made, defects or bubbles
occur, occasionally rendering the piece undesirable for marketing. It is known that, on
average, 1 in every 1000 of these items produced has one or more bubbles. What is the
probability that a random sample of 8000 will yield fewer than 7 items possessing
bubbles?
Q10: The probability that a person will die when he or she contracts a virus infection is
0.001. Of the next 4000 people infected, what is the mean number who will die?
Q11: The probability that a patient recovers from a delicate heart operation is 0.9.
What is the probability that exactly 5 of the next 7 patients having this operation
survive?
Q12: A traffic control engineer reports that 75% of the vehicles passing through a
checkpoint are from within the state. What is the probability that fewer than 4 of the
next 9 vehicles are from out of state?
Following problems cover the topic on Normal Distribution.
Q13: Given a standard normal distribution, find the area under the curve that lies
(a) to the left of
𝑧
= 1.39;
(b) to the right of
𝑧
=1 .96;
(c) between
𝑧
= −2.16 and
𝑧
= −0.65;
(d)
to the left of
𝑧
=1 .43;
(e)
to the right of
𝑧
= 0.89;
(f) between
𝑧
= −0.48 and
𝑧
=1 .74.
Q14: Find the value of
𝑧
if the area under a standard normal curve
(a) to the right of
𝑧
is 0.3622;
(b) to the left of
𝑧
is 0.1131;
(c) between 0 and
𝑧
, with
𝑧
>
0
, is 0.4838;
(d) between
𝑧
and
𝑧
, with
𝑧
>
0
, is 0.9500.

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CIVL/ECEN-403/MECH-328 Assignment # 4 Probability and Statistics for Engineers Summer 2019 - 20 Due Date: Sunday, August 30, 2020 Submit any 2 questions from Q1 - Q4, any 1 from Q5 – Q7, any 1 from Q8 – Q9, any 2 from Q10 – Q12, any 1 from Q13 – Q14, and any 2 from Q15 – Q17. (So, total = 9 ) Following problems covers the topic on Binomial Distribution. Q1: In a certain city district, the need for money to buy drugs is stated as the reason for 75% of all thefts. Find the probability that among the next 5 theft cases reported in this district, (a) exactly 2 resulted from the need for money to buy drugs; (b) at most 3 resulted from the need for money to buy drugs. Q2: According to a survey by the Administrative Management Society, one-half of U.S. companies give employees 4 weeks of vacation after they have been with the company for 15 years. Find the probability that among 6 companies surveyed at random, the number that give employees 4 weeks of vacation after 15 years of employment is (a) anywhere from 2 to 5; (b) fewer than 3. Q3: In testing a certain kind of truck tire over rugged terrain, it is found that 25% of the trucks fail to complete the test run without a blowout. Of the next 15 trucks tested, find the probability that (a) from 3 to 6 have blowouts; (b) fewer than 4 have blowouts; (c) more than 5 have blowouts. Q4: A nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to ...
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