Name That Distribution!
Suppose that milk is shipped to retail outlets
in boxes that hold 16 milk containers. One
particular box, which happens to contain 6
underweight containers, is opened for
inspection, and 5 containers are chosen at
random. What is the probability that at
least 1 of the 5 selected containers will be
underweight?
Ans: 0.9423
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 2 of the
next 5 vehicles are from out of state?
Ans: 0.6328
Suppose that a computer programmer, on
average, makes 3 errors in 500 lines of
code. What is the probability that the
programmer will make no errors in 250
lines of code?
Ans: 0.2231
There are 70 people in this class. 10 are
women. If we form a committee by
randomly choosing 5 people, what is the
probability that there will be no women on
the committee?
Ans: 0.4513
Ten is the average number of oil tankers
arriving each day at a certain port city.
The facilities can handle at most 15
tankers per day. What is the probability
that on a given day, tankers will have to
be turned away?
Ans: 0.0487
If 7 cards are dealt from an ordinary deck of
52 cards, what is the probability that
exactly 2 of them will be face cards (ace,
king, queen, jack)?
Ans: 0.3381
An Air Force intercept squadron consists of
16 planes that should always be ready for
immediate launch. However, there is a
probability of 0.25 that the engines of a
particular plane will not start at a given
attempt. If this happens, the mechanics
must wait 5 minutes before trying to start
the engine again. What is the expected
number of planes to immediately launch?
Ans: 12
Magnetic tape is slit into half inch widths
that are wound into cartridges. A slitter
assembly contains 48 blades. Five blades
are selected at random and evaluated
each day for sharpness. If any dull blades
are found the assembly is replaced.
If 10 of the blades are dull, what is the
probability that the assembly is replaced?
Ans: 0.7069
The number of cracks in a section of
interstate highway that are significant
enough to require repair averages 2 per
mile.
What is the probability that there will be at
least 1 crack in the next ½ mile of
highway?
Ans: 0.6321
A particularly long traffic light on your
morning compute is green 20% of the
time that you approach it. Over 20
mornings, what is the probability that the
light is green on exactly 4 days?
Ans: 0.2182
A small grocery store has 3 check-out
counters. The probability that no counters
are active on a Saturday morning is 0.05.
The probability that 1 counter is active is
0.25. The probability that 2 counters are
active is 0.50. What is the expected
number of counters to be active on
Saturday morning?
Ans: 1.85