Name:You may use a calculator on this quiz. You may not use a cell
phone or computer. Please read each question carefully, show your
work and give justifications for your answers. If you find that you
are spending a lot of time on one problem, leave it blank and move on
to the next. There are questions on both sides of this quiz paper.
Poisson: f(x) = λxe-λ/(x!)
Binomial: f(x) = n!/((x!)(n-x)!) * px
Converting to standard normal: z = (x - μ)/σ
Exponential: P(x < x0) = 1 -
(20 points) Give an example of a discrete random variable.
(20 points) Find the expected value of the probability function
shown below. Justify your answer.
(20 points) Suppose that the weight of a 5 lb bag of potatoes is
normally distributed with μ = 5.2 lb and σ = .2 lb. If a
randomly selected bag of potatoes has weight x, which is more likely:
x > 5 lb, or x < 5 lb? Justify your answer.
(20 points) An airline plans to install automated checkin kiosks
at an airport. They anticipate that 50 customers will use the kiosks
every hour, and that each customer will spend 6 minutes at a kiosk.
To determine how many kiosks to install, the airline wishes to
estimate the probability that 10 customers will all want to use a
kiosk during the same 5 minute interval. Would you use a Poisson
distribution or an exponential distribution to compute this
probability? Explain your choice.
(20 points) The probability of a proofreader detecting an error
in a manuscript is 95%. If two proofreaders check the same manuscript
which includes an error, what is the probability that at least one
of the two proofreaders detects the error?