Normal Distribution and Points

COMP 211 DATA AND SYSTEM MODELING (PROB/STAT) Spring 2012 Assignment #2 Due: Monday, 5pm, 4/16/2012 Total points: 200 (each question 20 points) Please submit a softcopy (in PDF format) of your assignment to WebCT before the deadline. Late penalty: within 24 hours after the deadline: ‐20%; after 24 hours: 0 point. Question 1: [20 points] A film-coating process produces films whose thickness are normally distributed with a mean of 110 microns and a standard deviation of 10 microns. For a certain application, the minimum acceptable thickness is 90 microns. (a) What proportion of films will be too thin? (b) To what value should the mean be set so that only 1% of the films will be too thin? (c) If the mean remains at 110, what must the standard deviation be so that only 1% of the films will be too thin? Question 2: [20 points] If a resistor with resistance R ohms carries a current of I amperes, the potential difference across the resistor, in volts, is given by V=IR. Suppose that I is lognormal with parameters μI =1 and σI2 = 0.2, R is lognormal with parameters μR =4 and σR2 = 0.1, and that I and R are independent. (a) Show that V is lognormally distributed , and compute the parametersμV and σV2 (Hint: ln V = ln I + ln R) (b) Find P(V < 200) (c) Find P(150≦V≦300) (d) Find the mean of V (e) Find the median of V (f) Find the standard deviation of V Question 3: [20 points] The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year. (a) Find the mean waiting time between accidents. (b) Find the standard deviation of the waiting times between accidents. (c) Find the probability that more than one year elapses between accidents. (d) Find the probability that less than one month elapses between accidents. (e) If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year? Question 4: [20 points] If T is a continuous random