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GuardWare Inc. has installed intrusion-detection devices on the campus of
a large university. The devices are very sensitive and, on any given
weekend, each one has a 10% chance of being mistakenly activated when
no intruder is present. Assume that the mistaken activations of different
devices are independent events.
There are six devices in the Administration building. Assume there will be
no intruder in that building next weekend.
(a) If two or more of the six devices in the Administration building are
activated during the same weekend, the system automatically signals
the police. What is the probability that this system will signal the
police next weekend?
Answer = (K) . Hint: remember the assumption.
(b) An intruder has a 5% chance of not activating the device located in the
President’s office. Campus police has obtained information about a
student prank in preparation and, as a result, estimates that there is a
20% chance that an intruder will visit the President’s office during next
Columbus Day weekend. If this device is activated during that
weekend, what is the probability that there is an intruder in the
President’s office? Answer = (L) .

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Suppose there are two types of drives, safe and unsafe. An insurance
company knows that 50% of drivers are unsafe, and an unsafe driver has a
40% chance of having an accident each year, but a safe driver has only a
10% chance of an accident each year. However, the company does not know
whether a new policy holder is safe or unsafe. Assume that for a given
driver, accidents are independent (and that drivers never have more than
one accident).

(a) What is the probability that a new policy holder has an accident the
first year?
Answer = (M) .
(b) What is the probability that a new policy holder that does not have an
accident in the first year is unsafe?
Answer = (N) .

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A large chain of fast-food restaurants tested four different advertising
programs to see if they differed in effectiveness. Four areas having similar
economic and demographic conditions were selected. Area 1 was assigned
program A; Area 2, Program B; Area 3, Program C; and Area 4 was
assigned Program D. The assignments of the programs were random. At
the end of one month, four restaurant units were selected randomly from

Area 1, four from Area 2, six from Area 3, and eight from Area 4. the gross
sales (in thousands of dollars) during the last week of the advertising
period are collected. Assuming that the data in the populations are
distributed normally, are there statistically significant differences among
the four advertising programs as measured by the gross sales? If you try to
answer this question, please set:
(a) The Null Hypothesis, and the Alternative Hypothesis. (5%)
You compute SST (Total Sum of Squares), SSG (Group Sum of Squares)
and SSE (Error Sum of Squares), and determine DF (Degrees of Freedom)
to test the hypothesis. The Level of Significance: α = 0.05 .
(b) Complete the following ANOVA table. (5%)

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