Review session outline
Intro/outline (5~10mn)
Sample questions (60~70min)
Open questions (~30min)
Closing remarks and evaluations (10 min)
1) An article in Information Security Technical Report, “Malicious Software—Past, Present and
Future” (Vol. 9, 2004, pp. 6–18), provided the following data on the top 10 malicious software
instances for 2002 (Fig. below). The clear leader in the number of registered incidences for the
year 2002 was the Internet worm “Klez,” and it is still one of the most widespread threats.
This virus was first detected on October 26, 2001, and it has held the top spot among
malicious software for the longest period in the history of virology. Suppose that 40 malicious
software instances are reported. Assume that the malicious sources can be assumed to be
independent. Round your answers to two decimal places (e.g. 98.76).
(a) What is the probability at least 3 instances are “Klez”?
(b) What is the probability that 2 or more instances are “Klez”?
(c) What is the mean and (d) standard deviation of the number of “Klez” instances among the
40 reported?
Because not all airline passengers show up for their reserved seat, an airline sells 126 tickets for
a flight that holds only 122 passengers. The probability that a passenger does not show up is
0.26, and the passengers behave independently. Round your answers to two decimal places (e.g.
98.76).
2
(a) What is the probability that every passenger who shows up gets a seat?
(b) What is the probability that the flight departs with empty seats?
(c) What are the mean and (d) standard deviation of the number of passengers who show up?
3) A telecommunication station is designed to receive a maximum of 9 calls per second. If the number
of calls to the station is modeled as a Poisson random variable with a mean of 12 calls per second,
what is the probability that the number of calls will exceed the maximum design constraint of the
station? Round your answers to four decimal places (e.g. 98.7654).
4) Flaws occur in mylar material according to a Poisson distribution with a mean of 0.04 flaw per
square yard. Round your answers to three decimal places (e.g. 98.765).
(a) If 27 square yards are inspected, what is the probability that there are no flaws?
(b) What is the probability that a randomly selected square yard has no flaws?
(c) Suppose that the mylar material is cut into 5 pieces, each being 1 yard square. What is
the probability that 3 or more of the 5 pieces will have no flaws?
5) Artificial Heart Part I. Medical researchers have developed a new artificial heart constructed
primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is
implanted in the patient's body, but the battery pack needs to be recharged about every four
hours. A random sample of 50 battery packs is selected and subjected to a life test. The
average life of these batteries is 4.05 hours. Assume that battery life is normally distributed
with standard deviation equal to 0.2 hours. Analysts wish to test the hypothesis that the mean
life of battery packs is bigger than 4 hours. Using Type I error probability = 0.05, what is the
numerical value of the test statistic taken to two decimal places?
b) Artificial Heart Part II. What is the p-value for the hypothesis test of Artificial Heart Part I?
Answer to three decimal places.
c) Artificial Heart Part IV. If the true population mean is 4.03 hours, what is the value of beta, the
probability of Type II error? Answer to three decimal places.
6) A particular brand of diet margarine was analyzed to determine the level of polyunsaturated fatty
acid (in percent). A sample of six packages resulted in the following data: 16.8, 17.2, 17.4, 16.9,
16.5, 17.1.
(a) Test the hypothesis that the mean is not 17.0, using the P-value approach (enter a value of 1 to
reject, enter a value of 2 to accept).
(b) Suppose that if the mean polyunsaturated fatty acid content is μ = 17.5, it is important to detect
this with probability at least 0.90. Is the sample size n = 6 adequate (if so enter a value of 1, if not
enter a value of 2)? Use the sample standard deviation to estimate the population standard
deviation σ.
Use α = 0.01. Find a 99% two-sided CI on the mean μ: (c) lower bound and (d) upper bound. Round
your answers to 2 decimal places.