Specify the probability distributions that could be used to
describe the situations listed below. Give parameters of the
distribution. Use the user-defined functions of the Random
Variables Add-in to answer the numerical
a. A communications satellite in orbit about the earth has
failed and NASA will send the space shuttle to fix it. On any
given flight there is a 75% chance that a successful repair
can be accomplished. What distribution can be used to answer
questions about the number of shuttle flights that will be required
to repair the satellite? What is the probability that more than
four flights will be required?
b. The number of arrivals to a convenience store during a two-hour
period has a Poisson distribution. The expected number of arrivals
during that period is 8. The store operator observes that it
has been 10 minutes since the last arrival. What distribution
describes the time until the next arrival? What is the probability
that the next arrival will occur before five minutes pass?
c. A student's grade on an exam can be approximated by a Normal
distribution with a mean value of 75 with a standard deviation
of 10. If the student takes four exams during the semester,
what distribution describes the sum of the four exam scores?
If a total score of at least 360 is required for an A grade,
what is the probability that the student will get an A?
d. A fortuneteller will make predictions about the next millennium.
Say the chance that any given prediction will come true is 80%.
The fortuneteller makes 20 predictions. What distribution describes
the number of predictions that will come true? What is the probability
that they all will come true?
e. The contractor is building your new house. He says that
it will be complete in 4 to 6 months, no more and no less. The
mode of the distribution is 5 months and the standard deviation
is 0.5 month. What distribution could be used to model this
situation? Give numerical values for the parameters of the distribution?