IS 310 Fall 2015 Assignment 3 Due date: 10/06/15 1. An experiment, which consists of tossing two fair coins, is performed. Let Y be the random variable, which denotes the number of heads appearing. What is the distribution of Y? (Find the probability of all the possible values Y can take). 2. A company employees receive an average of four non-work related emails per hour. Assume the Poisson distribution approximates the arrival of these emails. a. What is the probability that the president of the company received exactly two non-work-related email between 8am and 9am yesterday? b. What is the probability that she received two or more non-work- related emails between 8am and 9am yesterday? c. What is the probability that she did not receive any non-work-related email between 8am and 9am yesterday? 3. A survey reported that 35% of employees of company XYZ think that the company is loyal to them. Suppose 15 employees are selected randomly and will be interviewed about company loyalty. a. Is the selection of 15 employees a binomial experiment? Explain. b. What is the probability that none of the 15 employees will say that the company XYZ is loyal to them? c. What is the probability that 6 out of 15 employees will say the company is loyal to them? d. What is the probability that at least 2 out of the 15 employees will say the company is loyal to them? 4. A CD contains 10 songs; seven are classical and three are rock and roll. In a sample of five songs, what is the probability that exactly three are classical? Assume the samples are drawn without replacement. 5. A manufacturer knows from long experience that 3% of his production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 7 produced goods: a. None will need adjustment? b. At least one will need adjustment? c. More than two will need adjustment