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) = λ^{x}e^{-λ}/(x!) |
Binomial: f(x) = n!/((x!)(n-x)!) * p^{x}
(1-p)^{n-x} |

Converting to standard normal: z = (x - μ)/σ | Exponential: P(x < x_{0}) = 1 -
e^{-x0/μ} |

- (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.
**x**0 1 2 3 **f(x)**.3750 .1250 .1250 .3750 - (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?