Aids permitted: any calculators and one sheet of notes (8.5" x 11", one side only).
(a) Define probability.
(b) Give the full name of the person who discovered the Poisson distribution. What was the first application?
(c) Give John Tukey’s full name. When did he die? Name two statistical methods he developed.
If x is a data vector, the following R code will draw a well-known plot. What is this plot called? What is this plot used for?
plot(qnorm((1:length(x) - 0.5)/length(x)), sort(x))
The acceptable limits for the weight of a pellet you are producing are 96 g to 104 g. The standard deviation of weight is known to be 2.5 g. The process mean is usually 100 g but 10% of the time the process shifts and the mean is 102 g. If a pellet is sampled and found to be unacceptable, what is the probability that the process has shifted? State any assumptions you make.
The mean number of flaws in a coil of wire is known to be 0.2 per coil. A coil of wire is acceptable if it has no flaws. What is the probability that the first unacceptable coil you find is (a) the sixth one you test or (b) comes on or after the sixth test? If you have 100 coils, what is the probability that (c) at least 80 are acceptable? State any assumptions you make.
Display the following observed data on a stem and leaf plot and give the mode, median, mean, upper and lower hinges, and standard deviation. Repeat with the outlier removed.
2 2 0 2 4 0 2 2 2 2 2 2 4 2 4 4 22 2 2 3 2