You must SHOW ALL WORK for full credit (except for things computed entirely in R, in which case just state "from R"). Please staple your assignment if it is more than one page.

Required problems:

1) Problem 3.3 parts (a) and (b): Plastic parts are manufactured on an injection molding process. Some parts are classified as defective. The number of defective parts, Y, in a run of 1000 is a Binomial random variable with probability of defective, p=.005.
  a) Find the probability of no defective parts in a run of 1000.
  b) Find the probability of one or more defective parts in a run of 1000.
2) Problem 3.5: A simulation program calls a subroutine that generates a random number that is equally likely to be any value between 2.49 and 2.51.
  a) What is the probability that the subroutine generates a number between 2.492 and 2.498?
  b) What is the probability that the subroutine generates a number greater than 2.504?
3) Problem 3.7 part(a): The distribution of contact windows on CMOS circuits is normal with mean 3.5 microns and standard deviation .15 microns. Find the probability that a contact window diameter is between 3.3 and 3.6 microns. (Use Table A.3 on p. 750.)
4) Problem 3.13: North Dakota has an average of two blizzards per year in the five month period of November through March. (You will probably find it easier to use R for this question.)
  a) If the number of blizzards can be described by a Poisson distribution, what are the chances of having seven or more blizzards in the five month period?
  b) If the time between blizzards can be described by an exponential distribution, what are the chances of having at least four months without a blizzard? (Note: this question is saying that the mean number of blizzards in five months is two, so the rate of blizzards is 2/5, and the time between blizzards is exponential with mean 5/2, so what is the probability that this exponential is at least four?)