IE 3301-001 Engineering Probability Test #2 Practice Questions 1. The noon temperature in degrees Fahrenheit at Fairbanks, Alaska, during March is normally distributed with a mean of 10ºF and a standard deviation of 20ºF. Moreover, the noon temperature of one March day there is considered by meteorologists to be independent of the noon temperature of another March day. (a) What is the probability that a March day will have a temperature above 0ºF at noon? (b) Consider the first 16 days of March. (i) What is probability that at least 9 of the 16 days, will have noon temperatures above 0ºF? Write out the formulation, but do not calculate it. (ii) Calculate the expected value and standard deviation for the number days out of the 16 that will have a temperature above 0ºF at noon. 2. The weight of an engineering textbook is equally likely to be anywhere from 1 to 2 pounds. Suppose that you go to Amazon.com and start going randomly through its list of engineering texts, whose weights are given online, until you find a text that weighs more than 1.8 pounds. (a) What is the probability that any one engineering textbook will weigh more than 1.8 pounds? (b) What is the probability that you find such a book for the first time on the fourth text that you check on Amazon.com? 3. Suppose that the probability an item produced by a certain machine will be defective is 0.02. Find the probability that a sample of 100 items will contain at most 5 defective items. Use a Poisson approximation. 4. Consider an urn containing 14 colored balls, of which 5 are white, 4 are black, 3 are red, and 2 are green. A sample of 8 balls is taken. For the following, write out the formulations, but do not calculate them. (a) Suppose the sample is taken with replacement. What is the probability that the sample contains exactly 4 white, 2 black, 1 red, and 1 green ball? (b) Suppose the sample is taken without replacement. What is the probability that the sample contains exactly 4 white, 2 black, 1 red, and 1 green ball? 5. The annual inches of rainfall in a certain region follows a lognormal distribution with  = 3.5 and  = 0.1. Given ln(30) = 3.401 and ln(40) = 3.689, calculate the probability that between 30 and 40 inches of rain will fall in a year.6. Meteorites randomly strike the earth’s surface at an average rate of 90 meteorites per hour. (a) Find the probability that at least 4 meteorites strike the earth during a three-minute interval. (b) Find the probability that the time between two consecutive meteorites striking the earth is greater than 20 seconds. Derive the formulation using the c.d.f., but do not calculate it. (c) Find the probability that the time until 4 meteorites strike the earth is greater than 2 minutes. (d) Calculate the expected time until 4 meteorites strike the earth. 7. The publisher of a daily newspaper claims that 90% of its subscribers are under the age of 30. (a) Suppose a sample of 20 subscribers is selected at random. What is the exact probability that only one of the subscribers is over the age of 30? (b) Suppose now that a sample of 100 subscribers will be selected at random. Using a normal approximation, what is the probability that at least 8 subscribers are over the age of 30? 8. SAT total scores are approximately normally distributed with a mean of 1000 and a standard deviation of 200. What SAT score is needed to score in the 95 percentile of all