M203J Practice Quiz 3 Covering Chapters 15 and 16 Instructions: Answer each question, and when required explain your answer. Your explanation must be clear and complete. You may refer to your book, your notes and your homework papers. [1] (12 points) Consider a gumball machine with 3 red gumballs, 2 blues and a green. (a) What is the sample space if we choose two gumballs without regard to the order in which the two are chosen and record the colors of the chosen gumballs? How many ways are there to choose two gumballs? (b) How many pairs of gumballs are there where one gumball is blue and one is green? (c) If a pair of gumballs is chosen at random, what's the chance of choosing a pair consisting of one blue and one green gumball? (d) If a pair of gumballs is chosen at random, what's the chance of choosing a pair consisting of two red gumballs? (e) How many pairs of gumballs are there where the two gumballs have different colors? (f) If a pair of gumballs is chosen at random, what's the chance of choosing a pair consisting of two gumballs of different colors? [2] (3 points) An event has a probability of 70%. What are the odds against that event? [3] (9 points) Assume a test for a certain disease, which has a prevalence of 10%, has a sensitivity of 70% and a specificity of 90%. (a) For people who have the disease, what's the chance the test is negative? (b) For people who do not have the disease, what's the chance the test is negative? (c) If a randomly chosen test subject tests negative, what's the chance the subject nevertheless has the disease? Show how you obtain your answer. [4] (8 points) IQ's are normally distributed with mean 100 and standard deviation 15. (a) What percentage of the population has an IQ at or above 145? Show how you obtain your answer. (b) What percentage of the population has an IQ in the range 70 to 115? Show how you obtain your answer. [5] (8 points) Assume a newspaper runs a poll and finds p^ = 80% with a sample size of n = 900. (a) What is the margin of error? Show how you obtain your answer. (b) What sample size would be needed to obtain a margin of error of ± 2%? Show how you obtain your answer.