Research Methods Assignment 1 February 16 th 1. A manufacturing company has two suppliers for an electrical component used in its process: one in Mexico and one in China. The supplier ships 80% of all the electrical components used by the firm and has a defect rate of 5%. The Chinese supplier ships 20% of the electrical components used by the firm and has a defect rate of 8%. (a) Calculate the probability that an electrical component is defective, i.e. P(D). (b) Suppose that an electrical component is defective. What is the probability that component was shipped from Mexico. i.e., P(M\\D)? 2. Each week American Stores receives a shipment from a supplier. When the shipment arrives, a sample of 20 parts is randomly selected. If 2 or more of the sampled parts are defective, the shipment is rejected and returned to the supplier. Assume that a shipment arrives that actually has 4 percent defective parts and the distribution of defective parts is described by a binomial distribution. (a) What is the probability that there will be no defective parts in the sample? (b) What is the probability that the shipment will be accepted? 3. The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60. (a) What is the probability that there will be exactly 1 customer arriving in an hour? (b) What is the probability that there will be at most 1 customer arriving in an hour? (c) What is the probability that there will be at least 1 customer arriving in an hour? 4. The city council consists of 3 Democrats, 5 Republicans and 3 independents. Subcommittees are supposed to be randomly assigned from the council. Suppose the 5-member planning and zoning subcommittee is composed of 3 Democrats and 2 Republicans. What is the probability of this happening by chance alone? (Hint: Think about the underlying distribution.) 5. The change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $0.35 and a standard deviation of $0.33. Based on this information, answer the following questions. (a) What is the probability that a randomly selected stock will be lower by $0.40 or more? (b) What is the probability that a randomly selected stock will be higher by $0.40 or more? (c) What is the probability that the change in the price of a randomly selected stock will be less than $0.10