Questions 1 to 4
1. You are a project manager working on a movie called
Pirates of the Caribbean24. Your project is to produce and deliver a prop for
the set: a treasure chest. You estimate that manufacturing the chest in China
and filling it with gold will take between 10 days (you have 10% confidence
in this estimate) and 40 days (90% confidence) using normal distribution.
Delivery time should be the same in all cases. The director has requested that
you come up with an estimate with 90% confidence for both manufacturing and shipping
the treasure chest. Which of the following is your estimate?
A.

~80 days

B.

~50 days

C.

~63 days.

2. You are an artist drawing a wedding portrait of
Katie Holmes and Tom Cruise. You have two strategies: (1) Draw both of them
at the same time. This strategy will take 20 days. However, if at any time
during the 20 days, Katie and Tom decide that they do not like the portrait,
you have to start all over. The probability of them not liking your work is 60%.
(2) Draw Katie first and then Tom. This strategy will take 10 days for
each of them. If at any time during these 10 days Katie or Tom decides that
they do not like their portraits, you will need to restart your 10 days of
work. The probability of either of them not liking your work is 30%. Which strategy
should you use to complete the portrait faster (on average, taking into account
potential delays)?
A.

Both strategies will lead to the same duration.

B.

Strategy B is 17% faster than strategy A.

C.

Strategy B is 70% faster than strategy A.

3. Assume that you selected strategy 2 from the
previous question. There could be two scenarios: (a) Katie's and Tom's art
preferences are similar, so if Katie doesn't like the portrait, Tom probably won't
like it either; or (b) Katie's and Tom's preferences are different. What
is the project duration (on average, taking into account potential delays)?
A.

Situation A leads to a 50% faster completion of the portrait than situation B.

B.

Situation B leads to a 50% faster completion than situation A.

C.

Portrait completion times in situation A and B are about the same.

4. You are the organizer of a Rolling Stones concert
in your town, and you need to replace many amplifiers in the stadium where the
concert will take place. You know, based on independent testing, that only 1%
of all the amplifiers are defective, but you decide to test them anyway. The test
is 80% accurate; therefore, in 20% of the cases the amplifiers could pass the
test but stop working during the concerts. Your test indicates that a particular
amplifier is defective. What is the probability that the other amplifiers will
be defective?
